1. Problems of the Day Simplify each expression. 1. (9s3t2)(−3st)
2. 5xy2(x + y)
3. 7mn(m2 + 10mn – 2)
4. d(−3d + 5) + 15d
5. 4w(5w – 4) + 3(w2 – 2w + 6)
6. x(x + 3) – 2(x – 7)= x(x + 8)
−27s4t3
5x2y2 + 5xy3
7m3n + 70m2n2 – 14mn
−3d2 + 20d
23w2 – 22w + 18
x = 2

2. Multiplying Polynomials
Algebra 1 ~ Chapter 8.7
Multiplying Polynomials

3. This is what is called EXPAND or EXPANDING!
To multiply a binomial by a binomial, you can apply the Distributive Property more than once.
This is what is called EXPAND or EXPANDING!
(x + 3)(x + 2) = x(x + 2) + 3(x + 2)
= x(x + 2) + 3(x + 2)
= x(x) + x(2) + 3(x) + 3(2)
= x2 + 2x + 3x + 6
= x2 + 5x + 6

4. Example 1 – Simplify each expression
(x + 5)(x + 1)
= x(x) + x(1)
+ 5(x) + 5(1)
= x2 + 1x + 5x + 5
= x2 + 6x + 5
This expression is completely simplified. There are no like terms to combine.

5. Example 2 – Simplify each expression
(y + 3)(y – 7)
= y(y) + y(-7)
+ 3(y) + 3(-7)
= y2 + (-7y) + 3y + (-21)
= y2 – 4y – 21
This expression is completely simplified. There are no like terms to combine.

6. Example 3 – Simplify each expression
(a – 2)(a + 6)
= a(a) + a(6)
+ -2(a) + -2(6)
= a2 + 6a + (-2a) + (-12)
= a2 + 4a – 12
This expression is completely simplified. There are no like terms to combine.

7. Example 4 – Simplify each expression
(x – 4)(x – 5)
= x(x) + x(-5)
+ -4(x) + -4(-5)
= x2 + (-5x) + (-4x) + 20
= x2 – 9x + 20
This expression is completely simplified. There are no like terms to combine.

8. Example 5 – Simplify each expression
(2x + 3)(6x + 5)
= 2x(6x) + 2x(5)
+ 3(6x) + 3(5)
= 12x2 + 10x + 18x + 15
= 12x2 + 28x + 15
This expression is completely simplified. There are no like terms to combine.

9. Example 6 – Simplify each expression
(2x + 8)(5x – 4)
= 2x(5x) + 2x(-4)
+ 8(5x) + 8(-4)
= 10x2 + (-8x) + 40x + (-32)
= 10x2 + 32x – 32
This expression is completely simplified. There are no like terms to combine.

10. Example 7 – Simplify each expression
(3x2 – 2)(4x2 –5x+ 9)
= 3x2(4x2) + 3x2(-5x)
+ 3x2(9) -2(4x2) + -2(-5x)+ -2(9)
= 12x4 + (-15x3) + 27x2 +(-8x2) + 10x +(-18)
= 12x4 – 15x3 + 19x2 +10x – 18
This expression is completely simplified. There are no like terms to combine.

11. Ex. 8 – Find the area of each shape below.
a.) b.)
(4x – 3)
(x + 4)
(2x + 8)
A = ½(b · h)
A = ½(4x – 3)(2x + 8)
= ½(8x2 + 32x – 6x – 24)
= ½(8x2 + 26x – 24)
A = 4x2 + 13x – 12
A = b · h
A = (3x + 1)(x + 4)
= 3x2 + 12x + 1x + 4
A = 3x2 + 13x + 4

12. Lesson Wrap Up ~ Simplify each expression
1. (x + 2)(x – 8)
2. (a – 3)(a – 9)
3. (2x – 7)(5x – 4)
4. (3x – 5)(3x + 1)
5. Find the area of a triangle whose base is (6x + 4) and height is (x – 7).
x2 – 6x – 16
a2 – 12a + 27
10x2 – 43x + 28
9x2 – 12x – 5
A = 3x2 – 19x – 14

13. Assignment
Study Guide 8-7 (In-Class)
Skills Practice 8-7 (Homework)