Gr 9 MATH: Ch 5 Sum Algebraic Expressions

Play an AI-generated podcast conversation about this lesson

What is an algebraic expression?

A sequence of operations that can be described in words or diagrams (correct)

A diagram that represents a sequence of operations

A sequence of operations described in words

A sequence of operations that can only be described in words

When performing calculations in an algebraic expression, what operation should be done first if there are no brackets?

Subtraction and division

Exponents and roots

Addition and subtraction

Multiplication and division (correct)

What is a monomial in algebra?

An expression with one term (correct)

An expression with three terms

An expression with four terms

An expression with two terms

What is the purpose of brackets in an algebraic expression?

To perform calculations within the brackets first Signup and view all the answers

What is a trinomial in algebra?

An expression with three terms Signup and view all the answers

What is the symbol commonly used to represent a variable in an algebraic expression?

x Signup and view all the answers

What is the difference between equivalent algebraic expressions?

They have different sequences of operations but the same numerical value Signup and view all the answers

When writing algebraic expressions, what is the convention for writing a product?

The number comes first Signup and view all the answers

What is the order of operations when there are no brackets in an algebraic expression?

Multiplication and division, then addition and subtraction Signup and view all the answers

Why is the multiplication sign often omitted in algebraic expressions?

Because it is a convention Signup and view all the answers

What is the correct order of operations when evaluating an algebraic expression without brackets?

Multiplication and division, followed by addition and subtraction Signup and view all the answers

What is the term for an expression with one term, such as 3x^2?

Monomial Signup and view all the answers

What is the result of expanding the product of two binomials (x + a)(x + b)?

x^2 + (a + b)x + ab Signup and view all the answers

What is the general form for squaring a binomial (a + b)?

a^2 + 2ab + b^2 Signup and view all the answers

What is the result of dividing a polynomial by a monomial?

Each term in the polynomial is divided by the monomial Signup and view all the answers

What is the term for a fixed value in an algebraic expression, such as 4 in 5x + 4?

Constant Signup and view all the answers

What is the distributive property of division?

(x + y) / z = (x / z) + (y / z) Signup and view all the answers

What is the result of expanding the product of two binomials (x - y)(x + z)?

x^2 + (z - y)x - yz Signup and view all the answers

What is the purpose of substituting specific values for variables in algebraic expressions?

To check for equivalence and simplification Signup and view all the answers

What is the term for a sum of two terms, such as 5x + 4?

Binomial Signup and view all the answers

What is the correct order of operations when evaluating an algebraic expression with brackets?

Perform the calculations within the brackets first Signup and view all the answers

What is the name of the property that allows us to rewrite an algebraic expression in a different form?

Distributive property Signup and view all the answers

What is the term for an algebraic expression that has the same numerical value as another expression for any given value of the variable?

Equivalent expression Signup and view all the answers

Why is it important to follow the order of operations when evaluating algebraic expressions?

To ensure accuracy Signup and view all the answers

What is the purpose of writing algebraic expressions?

To represent sequences of calculations Signup and view all the answers

What is the name of the diagram used to represent the sequence of operations in an algebraic expression?

Flow diagram Signup and view all the answers

What is the purpose of parentheses in an algebraic expression?

To clarify the order of operations Signup and view all the answers

What is the correct way to write a product in an algebraic expression?

With the known number first Signup and view all the answers

What is the term for the numerical coefficient in a monomial?

Coefficient Signup and view all the answers

What is the purpose of describing sequences of calculations with algebraic expressions?

To represent sequences of operations Signup and view all the answers

Which of the following is NOT a convention for writing algebraic expressions?

Write the multiplication sign explicitly Signup and view all the answers

What is the result of expanding the product of two binomials (x + 2)(x + 3)?

x^2 + 5x + 6 Signup and view all the answers

What is the result of simplifying the expression 2x + 3x - 4x + x?

2x - 4 Signup and view all the answers

What is the result of dividing the polynomial 6x^2 + 12x by the monomial 2x?

3x + 6 Signup and view all the answers

What is the result of expanding the product of two binomials (x - 2)(x + 1)?

x^2 - x - 2 Signup and view all the answers

What is the result of simplifying the expression 3(x + 2) + 2(x - 1)?

5x + 4 Signup and view all the answers

What is the result of squaring the binomial (x + 4)?

x^2 + 8x + 16 Signup and view all the answers

What is the result of simplifying the expression 2x^2 + 3x + 1 - (x^2 + 2x + 1)?

x^2 + x Signup and view all the answers

What is the result of dividing the polynomial 2x^3 + 4x^2 + 6x by the monomial x?

2x^2 + 4x + 6 Signup and view all the answers

What is the result of simplifying the expression 3x^2 + 2x - 5 - (2x^2 + 3x - 1)?

x^2 - x - 4 Signup and view all the answers

Simplify the expression $(x + 3)(x + 2) - (x + 1)^2$

$x^2 + 5x + 2$ Signup and view all the answers

What is the result of dividing the polynomial $4x^2 - 2x + 2$ by the monomial $x - 1$?

$4x + 2$ Signup and view all the answers

What is the result of expanding the product of two binomials $(x + 2y)(x - 3y)$?

$x^2 - 7y^2$ Signup and view all the answers

What is the result of simplifying the expression $2x^2 + 5x - 3 - (x^2 + 2x - 1)$?

$x^2 + 3x - 2$ Signup and view all the answers

What is the result of squaring the binomial $(x + 2y)^2$?

$x^2 + 4y^2 + 4xy$ Signup and view all the answers

What is the result of expanding the product of two binomials (x + 3)(x + 5)?

x^2 + 8x + 15 Signup and view all the answers

What is the result of simplifying the expression 2x^2 + 5x - 3x^2 + 2x?

-x^2 + 7x Signup and view all the answers