Problems of the DaySimplify 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)

5x2y2 + 5xy3

−27s4

t3

7m3n + 70m2n2 – 14mn

−3d2 + 20d

23w2 – 22w + 18

x = 2

Algebra 1 ~ Chapter 8.7

Multiplying Polynomials

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

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.

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.

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.

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.

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.

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.

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.

Ex. 8 – Find the area of each shape below.

a.) b.) (3x + 1)

(x + 4)

A = b · h

A = (3x + 1)(x + 4)

= 3x2 + 12x + 1x + 4

A = 3x2 + 13x + 4

(4x – 3)

(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

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

10x2 – 43x + 28

a2 – 12a + 27

9x2 – 12x – 5

A = 3x2 – 19x – 14

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