Algebraic Expressions
Evaluate the expression for x = 5: 3x + 2
17
Write an expression for "nine less than a number x."
x - 9
State the commutative property of addition.
The commutative property of addition states that changing the order of addends does not change the sum. For example: a+b=b+a
Apply the distributive property to simplify: 3(2x + 4).
3(2x+4) = 3⋅2x+3⋅4 = 6x+12
Factorize the expression: 6x + 9.
Factor out the common factor (3):
6x+9 = 3(2x+3)
Simplify the expression: 4y + 2y - 5y
y
Translate "the sum of a number y and 8" into an algebraic expression.
y + 8
Explain the associative property of multiplication with an example.
The associative property of multiplication states that changing the grouping of factors does not change the product. For example: (a⋅b)⋅c=a⋅(b⋅c)
Expand the expression using the distributive property: 2(3y - 7).
2(3y−7) = 2⋅3y−2⋅7 = 6y−14
Factor out the greatest common factor in the expression: 12a + 16.
Factor out 4:
12a+16 = 4(3a+4)
If n = 7, what is the value of the expression 2n - 5?
9
Express "twice a number n increased by 5" as an algebraic expression.
2n + 5
Identify the property demonstrated: 8 + 3 = 3 + 8
This demonstrates the commutative property of addition.
Combine like terms in the expression: 5(2a + 3) + 4(a - 1).
5(2a+3)+4(a−1) = 10a+15+4a-4 = 14a+11
Factor out the common factor: 9x + 36.
Factor out 9:
9x+36 = 9(x+4)
What is the sum of 3p + 2 and 4p - 1 when p = 2?
15
Write an expression for "three times the difference between a number m and 4."
3(m - 4)
Describe the distributive property of multiplication over addition.
The distributive property states that for any numbers a, b and c.
a⋅(b+c)=a⋅b+a⋅c
Using the distributive property, simplify: 4(2x + 3) + 2(3x - 1).
4(2x+3)+2(3x−1) = 8x+12+6x-2 = 14x+10
Factor the expression using the GCF:
27x - 18y
Factor out the 9:
9(3x - 2y)
Find the value of 5(x + 3) when x = 4.
35
Create an expression for "the product of a number p and 6 decreased by 9."
6p - 9
What is the identity property of multiplication?
The identity property of multiplication states that multiplying a number by 1 gives the number itself: a⋅1=a
Using the distributive property, simplify: 5(x + 3x) + 4x(x + 2).
5(x+3)+4x(x+2) = 5x+15+4x2+8x = 4x2+13x+15
Factor the expression using the GCF:
42a - 14b
Factor out the 14:
14(3a - b)