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Questions and Answers
What expression represents 'x increased by 12'?
What expression represents 'x increased by 12'?
The expression for 'y decreased by 7' is (7 - y).
The expression for 'y decreased by 7' is (7 - y).
False
What is the sum of x and y represented as?
What is the sum of x and y represented as?
x + y
The product of x and y added to their sum is _____ + (x + y).
The product of x and y added to their sum is _____ + (x + y).
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Which of the following represents '5 times x added to 7 times y'?
Which of the following represents '5 times x added to 7 times y'?
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X cubed less than y cubed is represented as y^2 - x^2.
X cubed less than y cubed is represented as y^2 - x^2.
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What is the expression for 'one third of x multiplied by the sum of a and b'?
What is the expression for 'one third of x multiplied by the sum of a and b'?
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Match the algebraic expressions to their descriptions:
Match the algebraic expressions to their descriptions:
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What is the final simplified result of the expression $- a - [2b - a]$?
What is the final simplified result of the expression $- a - [2b - a]$?
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The final result after simplifying the expression $5x - [4y - {7x - (3z - 2y) + 4z - 3(x + 3y - 2z)}]$ is $9x - 11y + 7z$.
The final result after simplifying the expression $5x - [4y - {7x - (3z - 2y) + 4z - 3(x + 3y - 2z)}]$ is $9x - 11y + 7z$.
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What is the result of simplifying the expression $2a - [5b - 6a]$?
What is the result of simplifying the expression $2a - [5b - 6a]$?
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After removing the innermost grouping symbols from the expression $2a - [4b - {6a - b}]$, the next simplified result is __________.
After removing the innermost grouping symbols from the expression $2a - [4b - {6a - b}]$, the next simplified result is __________.
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Match the following expressions with their simplified results:
Match the following expressions with their simplified results:
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What is the result of the expression $bbb*…$ repeated 15 times?
What is the result of the expression $bbb*…$ repeated 15 times?
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The expression $6 * x * x * y * y$ simplifies to $6x^2y^2$.
The expression $6 * x * x * y * y$ simplifies to $6x^2y^2$.
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What is the solution for $(2×2)-(3×3)$ when $a=2$ and $b=3$?
What is the solution for $(2×2)-(3×3)$ when $a=2$ and $b=3$?
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The e______pression $3* z * z * z * y * y * $ can be simplified to $3z^3y^2$. Fill in the missing variable.
The e______pression $3* z * z * z * y * y * $ can be simplified to $3z^3y^2$. Fill in the missing variable.
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Match the following substitutions with their results:
Match the following substitutions with their results:
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What is the final result when substituting $a = 2$ and $b = 3$ in $22 + (2 * 3)$?
What is the final result when substituting $a = 2$ and $b = 3$ in $22 + (2 * 3)$?
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The result of the expression $23 - 33$ when $a = 2$ and $b = 3$ is $-19$.
The result of the expression $23 - 33$ when $a = 2$ and $b = 3$ is $-19$.
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What is the simplified form of $14 * a * a * a * a * b * b * b$?
What is the simplified form of $14 * a * a * a * a * b * b * b$?
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The result of $(−2)^2 + (−1)^2 − (3)^2$ is __________.
The result of $(−2)^2 + (−1)^2 − (3)^2$ is __________.
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What is the simplified expression for the combination of terms $-3a - 3b + 8a - 12b - 2a + b$?
What is the simplified expression for the combination of terms $-3a - 3b + 8a - 12b - 2a + b$?
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The expression $-4x^2 + (x^2 - 3) - (4 - 3x^2)$ simplifies to $x^2 - xy$.
The expression $-4x^2 + (x^2 - 3) - (4 - 3x^2)$ simplifies to $x^2 - xy$.
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What is the result after removing grouping symbols from the expression $a - [2b - {3a - (2b - 3c)}]$?
What is the result after removing grouping symbols from the expression $a - [2b - {3a - (2b - 3c)}]$?
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The expression $86 - [15x - 7(6x - 9) -2{10x - 5(2 - 3x)}]$ simplifies to _____ .
The expression $86 - [15x - 7(6x - 9) -2{10x - 5(2 - 3x)}]$ simplifies to _____ .
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Match the expressions with their simplified forms:
Match the expressions with their simplified forms:
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In the expression $-4x^2 + ext{{{group}}}$, which group should be removed first?
In the expression $-4x^2 + ext{{{group}}}$, which group should be removed first?
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The expression $a - [4b - 3a - 3c]$ simplifies to $-4b + 4a + 3c$.
The expression $a - [4b - 3a - 3c]$ simplifies to $-4b + 4a + 3c$.
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What is the simplified form of the expression $3a - [5b - (2a - 3b)]$?
What is the simplified form of the expression $3a - [5b - (2a - 3b)]$?
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What is the simplified result of the expression $3x + 7x$?
What is the simplified result of the expression $3x + 7x$?
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The expression $7y + (-9y)$ simplifies to $2y$.
The expression $7y + (-9y)$ simplifies to $2y$.
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What is the sum of the expressions $(3a - 2b + 5c)$ and $(2a + 5b - 7c)$, when also subtracting $(-a - b + c)$?
What is the sum of the expressions $(3a - 2b + 5c)$ and $(2a + 5b - 7c)$, when also subtracting $(-a - b + c)$?
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The result of $6a^3 - 4a^3 + 10a^3 - 8a^3$ equals _______.
The result of $6a^3 - 4a^3 + 10a^3 - 8a^3$ equals _______.
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Match the expressions with their simplified results:
Match the expressions with their simplified results:
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What is the simplified result of $2x^2 - 8xy + 7y^2 - 8xy^2 + 2xy^2 + 6xy - y^2 + 3x^2 + 4y^2 - xy - x^2 + xy^2$?
What is the simplified result of $2x^2 - 8xy + 7y^2 - 8xy^2 + 2xy^2 + 6xy - y^2 + 3x^2 + 4y^2 - xy - x^2 + xy^2$?
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The expression $2 + x - x^2 + 6x^3$ can be rearranged to $6x^3 - x^2 + x + 2$.
The expression $2 + x - x^2 + 6x^3$ can be rearranged to $6x^3 - x^2 + x + 2$.
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The result of the expression $- x^3 + y^3 - z^3 + 3xyz$ when simplified is _______.
The result of the expression $- x^3 + y^3 - z^3 + 3xyz$ when simplified is _______.
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What is the result of the expression $5x + (-5x)$?
What is the result of the expression $5x + (-5x)$?
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What is the result of adding the following expressions: $(9x + 4y - 5z) + (3x + 3y - 4z)$?
What is the result of adding the following expressions: $(9x + 4y - 5z) + (3x + 3y - 4z)$?
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It is necessary to change the sign of each term of the expression to be subtracted to compute the difference between two expressions.
It is necessary to change the sign of each term of the expression to be subtracted to compute the difference between two expressions.
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What is the simplified form of $4x - (3y - x + 2z)$?
What is the simplified form of $4x - (3y - x + 2z)$?
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The simplified result of $2x - 3y + 4z - (2x + 5y - 6z + 2)$ is __________.
The simplified result of $2x - 3y + 4z - (2x + 5y - 6z + 2)$ is __________.
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Match the following expressions with their simplified forms:
Match the following expressions with their simplified forms:
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What does the expression $1 - (2x - 3y - 4)$ simplify to?
What does the expression $1 - (2x - 3y - 4)$ simplify to?
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Simplifying the expression $a^2 + b^2 + 2ab - a^2 - b^2 + 2ab$ yields $4ab$.
Simplifying the expression $a^2 + b^2 + 2ab - a^2 - b^2 + 2ab$ yields $4ab$.
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When calculating how much $2x - 3y + 4z$ is greater than $2x + 5y - 6z + 2$, the expression to be subtracted from the first is __________.
When calculating how much $2x - 3y + 4z$ is greater than $2x + 5y - 6z + 2$, the expression to be subtracted from the first is __________.
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Study Notes
Algebraic Expressions
- Algebraic expressions combine constants and variables using mathematical operations.
- Variables represent unknown values, and constants are fixed numerical values.
- Exponents: Represent repeated multiplication of a variable.
- A common mathematical operation is increasing or decreasing by a number, for instance multiplying by or dividing by, and taking a difference and sum.
Solving Algebraic Expressions
- Given different expressions, identify and perform calculations according to the question to arrive at the solution.
- Evaluate the algebraic expressions when specific values are assigned to the variables.
- Substitution: Replace variables with their assigned values.
- Order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
Like Terms
- Like terms have the same variables raised to the same power.
- Combine like terms by adding or subtracting their coefficients.
Simplifying Expressions
- Simplify expressions by combining like terms and performing operations.
- Apply order of operations when needed.
Classifying Expressions
- Monomial: A single term (e.g., 3x, 5y²).
- Binomial: Two terms (e.g., 2x + 3y, 7x² - 2).
- Trinomial: Three terms (e.g., 4x² - 5x + 7, -6 - 2y + 3z).
- If an expression contains more than three terms, it does not fall into these categories.
Constants in an Expression
- The constant terms in an expression are the fixed values.
- In the expression 3x² + 5x + 8, the constant term is 8.
Coefficient of a Variable
- The numerical factor in a term is called the coefficient.
- In the term -7x, the coefficient is -7.
Numerical Coefficients
- The numerical factor in a term is termed as the numerical coefficient.
- In the term 8xy, the numerical coefficient is 8.
Examples of Algebraic Expressions with Solutions
-
Example 1: 5x + 2y = 100. Solve for x with y= 10.
- Substituting y = 10: 5x + 2(10) = 100
- Simplifying: 5x + 20 = 100
- Isolate x: 5x = 80, and x = 16
-
Example 2: x² - 4x = 5x. Find x.
- Rearrange to 𝑥²⁻9𝑥 = 0
- Factorize to 𝑥(𝑥−9) = 0
- So either x=0 or x = 9
-
Example 3: The term "twice x increased by y" is equivalent to 2𝑥+𝑦.
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Description
This quiz focuses on algebraic expressions, their components, and solving techniques. Learn about variables, constants, exponents, and the importance of order of operations. Engage in identifying and evaluating expressions through substitution and combining like terms.
