Lesson 8-7

Multiplying Polynomials

FOIL Method-F = the First termsO = the Outer termsI = the Inner termsL = the Last terms

(x + 3) (x - 2)

FOIL Method-F = the First termsO = the Outer termsI = the Inner termsL = the Last terms

(x - 5) (x + 7)

F O I Lx x x 7 -5 x -5 7

x2

+ + +

+ + +7x -5x -35

x2 + 2x -35

Find each product.

)12)(6( a. −− zz

)82)(45( b. +− xx

The Area A of a trapezoid is one-half the height h times the sub of the bases, b1 and b2. Write

an expression for the area of the trapezoid.3x - 7

x + 2

2x + 1

h = x + 2b1 = 3x - 7b2 = 2x + 1

€

A = 1

2 • h • (b1 +b2)

A = ½h(b1+b2) = ½(x+2)[(3x - 7)+(2x +1)] = ½(x+2)(5x -

6) = ½[x(5x) + x(- 6) + 2(5x) + 2(-6)]

= ½(5x2 - 6x + 10x -12) = ½(5x2 + 4x -12)

€

=5

2x 2 + 2x − 6

The Area A of a triangle is one-half the height h times the base. Write an expression for the

area of the triangle.

6x+4

X-7

The Distributive PropertyEx. 4

(4x + 9) (2x2 - 5x + 3)4x(2x2 - 5x + 3) + 9(2x2 - 5x + 3)

8x3 - 20x2 + 12x + 18x2 - 45x + 27

8x3 - 2x2 - 33x + 27

(y2 - 2y + 5) (6y2 - 3y + 1)

y2(6y2 - 3y + 1) - 2y (6y2 - 3y + 1) + 5(6y2 - 3y + 1)

6y4 -3y3 + y2 -12y3 + 6y2 -2y + 30y2 -15y + 5

6y4 -15y3 + 37y2 - 17y + 5

Find each product.

)112)(43( a. 2 +−+ aaa

)13)(972( b. 22 −+++ bbbb