Page 140 - Math Course 2 (Book 1)

Factoring Binomials

Use Differences of Two Squares
MO. 4 - L5b

Solving with Difference of GEOMETRY

Squares A square with side length x is cut
from a right triangle shown at the
right. What value of x will result in 16
1
Let’s Begin a f gure that is of the area of the x
3
original triangle? Show how you x
8
arrived at your answer.
Solve Equations by Factoring
Words A is the area of the triangle minus the
Example area of the square that is to be removed.

4
2
In the equation q – 25 = y, which is a value of q Variables Let x = the length of the side of the
when y = 0? square.
2 4 2
A. B. C. 0 D.– 1
25 25 5 The area of the triangle is • 16 • 8
2
or 64 square units and the area of the
4
2
Factor as the difference of squares. square is x • x or x2 square units.
q –
25
Solve the Test Item Equation A = 64 – x 2

2
q – 4 = y Original equation A = 1 A Translate the verbal
25 6 0 statement.
4 2 1 2
2
q – = 0 Replace y with 0. 64 – x = (64) A = 64 – x and A = 64
25 6 0
2
64 – x = 48 Simplify.
2
4
2
2
2
2
q – 2 = 0 q = q • q and = •
5 25 5 5
2
64 – x – 48 = 0 Subtract 48 from
each side.

q + 2 q – 2 = 0 Factor the difference of
5 5
2
squares. 16 – x = 0 Simplify.

of squares.
q + 2 = 0 or q – 2 = 0 Zero Product Property (4 + x)(4 – x) = 0 Factor the difference
5 5

q =– 2 q = 2 Solve each equation. 4 + x = 0 or 4 – x = 0 Zero Product Property.
5 5
x = –4 x = 4 Solve each equation.
2 2 Since the length cannot be
–
The roots are and .
Answer 5 5 Answer negative, the only reasonable
The correct answer is D. solution is 4.

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