Algebraic Expressions and Solving Techniques

The result of adding 12 to the variable x.

The result of subtracting 7 from the variable y.

The result of multiplying the variable x by itself.

The result of multiplying the variable x by 3 and then adding the square of the variable y.

The result of dividing the variable x by 8 and then multiplying the quotient by the variable y.

The result of adding 5 times the variable x to 7 times the variable y.

The result of subtracting twice the variable y from the variable x.

The result of dividing the variable y by 5.

To find how much greater one expression is than another, subtract the smaller expression from the larger one.

When subtracting an expression, change the sign of each term in that expression and then add.

To simplify an expression with parentheses preceded by a '-' sign, remove the parentheses and change the sign of each term within the parentheses.

Combining like terms involves adding or subtracting coefficients of terms with the same variables and exponents.

An algebraic expression can be simplified by combining like terms after removing parentheses.

To find how much one expression exceeds another, subtract the smaller expression from the larger one.

When simplifying algebraic expressions, change the signs of terms within parentheses preceded by a '-' sign.

Combining like terms involves grouping terms with the same variables and exponents and then adding or subtracting their coefficients.

A variable raised to a power indicates repeated multiplication of the variable by itself.

A coefficient is the number that multiplies a variable or a product of variables.

A power of a variable represents the number of times the variable is multiplied by itself. For example, x raised to the power of 3 (x^3) means x multiplied by itself three times: x * x * x.

To evaluate an expression, you substitute the given values for variables and then perform the calculations according to the order of operations (PEMDAS/BODMAS).

Substituting values involves replacing variables in an expression with their numerical values. For example, if x = 2, then substituting x in "2x + 3" would give "2(2) + 3".

The order of operations (PEMDAS/BODMAS) governs the sequence in which operations are performed in an expression. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS stands for Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

To simplify an expression, you combine like terms and perform calculations according to the order of operations.

Like terms are terms in an expression that have the same variable and exponent, allowing them to be combined. For example, 2x and 3x are like terms, but 2x and 3x^2 are not.

Combining like terms involves adding or subtracting coefficients of terms with the same variable and exponent.

An equation states that two expressions are equal. For example, 2x + 5 = 15.

Adding algebraic expressions involves combining like terms. Like terms have the same variables and exponents. Example: 3x and 7x are like terms, but 3x and 7y are not.

Combine the coefficients of like terms to find the sum. Example: 3x + 7x = (3 + 7)x = 10x

Subtracting algebraic expressions involves changing the sign of each term in the expression being subtracted and then adding the expressions. Example: 5x - 2y is the same as 5x + (-2y)

When subtracting like terms, combine the coefficients with the opposite sign of the term being subtracted. Example: 3x - 5x = 3x + (-5)x = -2x

When subtracting algebraic expressions with multiple terms, distribute the negative sign to each term in the expression being subtracted - changing the sign before each term. Example: (3x - 2y) - (x + 4y) becomes 3x - 2y - x - 4y

Rearrange the terms of an expression so that like terms are grouped together. Then, combine the coefficients of like terms to simplify the expression. Example: (2a + 5b - c) + (3a - 2b + 4c) can be rearranged as 2a + 3a + 5b - 2b - c + 4c.

When adding or subtracting algebraic expressions, we can only combine terms with the same variables and powers (exponents). Example: We can combine 3x^2 and 5x^2 but not 3x^2 and 5x.

Subtracting expressions with multiple terms involves changing the sign of each term in the expression being subtracted and then combining like terms. Example: (2x^2 - 3xy + 5y^2) - (-x^2 + xy - 2y^2) becomes 2x^2 - 3xy + 5y^2 + x^2 - xy + 2y^2

Removing grouping symbols in expressions involves simplifying the expression by applying the order of operations and combining like terms.

When a minus sign precedes parentheses, we distribute the minus sign to each term inside. This changes the sign of each term.

To remove nested grouping symbols, we work from the innermost to the outermost.

Combining like terms simplifies the expression by grouping similar terms together.

Expressions can be simplified using the order of operations, including removing grouping symbols, distributing, and combining like terms.

In expressions involving variables, we group terms with the same variables and exponents together.

Simplifying expressions requires understanding the order of operations, distributing signs, and combining like terms.

Removing the innermost grouping symbols first, then proceeding outward to the outermost symbols. This method simplifies complex expressions by breaking them down systematically.

Multiplying a number or variable by the terms within parentheses. It's like distributing the number or variable to each term inside.