7.4 – Expanding and Factoring Algebraic Expressions
Objective…
Part A: Use the distributive property to expand algebraic expressions
a)
Expand 2(r + 8)
2(r + 8)
means
Bar model…
Rearrange bar model…
Using the distributive property…
b)
Expand 3(k + 6)
3(k + 6)
means
Bar model…
Rearrange bar model…
Using the distributive property…
7.4 – Expanding and Factoring Algebraic Expressions
Practice…expand each expression
1)
3(x + 4) = _______________
4)
5(y – 3) = _______________
2)
6(2x + 3) = _______________
5)
4(4y – 1) = _______________
3)
2(7 + 6x) = _______________
6)
9(5x – 2) = _______________
Practice…state whether each pair of expressions of equivalent: YES or NO
1)
6(x + 5) and 6x + 30: _______________
2)
7(x + 3) and 21 + 7x: _______________
3)
4(y – 4) and 4y – 4: _______________
4)
3(y – 6) and 18 – 3y: _______________
Part B: Algebraic expressions can be factored by taking out a common factor

You can expand the expression 3(4z + 1) by writing it as _______________.

You can also start with the expression 12z + 3 and write is as _______________.

When you write 12z + 3 as _______________ you have factored 12z + 3.
a)
Factor 2y + 10
List factors of List factors of
2y
10
Rewrite to factor
Check by expanding the
expression
7.4 – Expanding and Factoring Algebraic Expressions
b)
Factor 6z -9
List factors of List factors of
6z
9
Rewrite to factor
Check by expanding the
expression
Practice…factor each expression – think trees!
1)
3x + 3 = _______________
6)
4x + 6 = _______________
2)
8 + 6y = _______________
7)
5y – 10 = _______________
3)
4 – 10z = _______________
8)
12 – 8x = _______________
4)
8f + 6 = _______________
9)
12m – 8 = _______________
5)
15 + 5q = _______________
10)
32m – 40 = _______________
7.4 – Expanding and Factoring Algebraic Expressions
Practice…state whether each pair of expressions are equivalent: YES or NO
1)
8x + 6 and 2(4x + 3): _______________
2)
5x – 10 and 5(x – 5): _______________
3)
3(x + 5) and 15 + 3x: _______________
4)
3(y + 6) and 18 + 3y: _______________
5)
4(y – 4) and 16 – 4y: _______________
6)
12 – 8y and 4(2y – 3): _______________
CHALLENGE…think! Simplify each expression. Then factor the expression.
1) 14m + 13 – 8m – 1
2) 8(y + 3) + 6 – 3y
3) 4(3y + 7) + 5(8 + 6y)