Page 105 - Math Course 2 (Book 1)

Polynomials: Multiplication

GEOMETRY
Let’s Begin The area A of a triangle is one half
the height h times the base b.
Write an expression for the x – 7
area of the triangle.
FOIL Method 6x + 4

Explore Identify the height and the base.
Examples h = x – 7
b = 6x + 7

Find (z – 6)(z – 12). Plan Now write and apply the formula.

F L Area equals one half height times base.

(z – 6)(z – 12) A = 1 h • b
2
I
0 1
F O I L Solve A = hb. Original formula.
2
= z(z) + z(–12) + (–6)z + (–6)(–12)
1
A = (x – 7) (6x + 4)
2
= z – 12z – 6z + 72 Multiply. 2 Substitution.
2
= z – 18z + 72 Combine like terms. 1
A = [x (6x) + x(4) –7(6x) –7 (4)]
2
FOIL Method.
2
Answer z – 18z + 72
1
2
A = (6x + 4x –42x –28)
2
Find (5x – 4)(2x + 8). Multiply.
(5x – 4)(2x + 8) 1
2
A = (6x – 38x – 28)
2
F O I L Combine like terms.
= (5x)(2x) + (5x)(8) + (–4)(2x) + (–4)(8)
2
A = 3x – 19x – 14
2
= 10x + 40x – 8x – 32 Multiply. Distributive Property.
2
= 10x + 32x – 32 Combine like terms.
The area of the triangle is
2
Answer 10x + 32x – 72 Answer
2
3x – 19x – 14 square units.

Your Turn!

FOIL Method

Find (x + 2)(x – 3). Find (3x + 5)(2x – 6).

2
2
A. x + x – 6 A. 5x – 8x + 30
2
2
B. x – x – 6 B. 6x + 28x – 1
2
2
C. x + x + 6 C. 6x – 8x – 30
2
D. x + x + 5 D. 6x – 30
Answer Answer

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