Problems of the Day Simplify each expression 1

Problems of the Day Simplify each expression. 1. (9 s 3 t 2)(− 3 st) − 27 s 4 t 3 2. 5 xy 2(x + y) 5 x 2 y 2 + 5 xy 3 3. 7 mn(m 2 + 10 mn – 2) 4. d(− 3 d + 5) + 15 d 7 m 3 n + 70 m 2 n 2 – 14 mn − 3 d 2 + 20 d 5. 4 w(5 w – 4) + 3(w 2 – 2 w + 6) 23 w 2 – 22 w + 18 6. x(x + 3) – 2(x – 7)= x(x + 8) 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) + x(2) + 3(x) + 3(2) = x 2 + 2 x + 3 x + 6 = x 2 + 5 x + 6

Example 1 – Simplify each expression (x + 5)(x + 1) = x(x) + x(1) + 5(x) + 5(1) = x 2 + 1 x + 5 = x 2 + 6 x + 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) = y 2 + (-7 y) + 3 y + (-21) = y 2 – 4 y – 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) = a 2 + 6 a + (-2 a) + (-12) = a 2 + 4 a – 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) = x 2 + (-5 x) + (-4 x) + 20 = x 2 – 9 x + 20 This expression is completely simplified. There are no like terms to combine.

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

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

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

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

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

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