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Factoring the Difference of Two Squares
WHAT TO DO:
HOW TO DO IT:
1. Factor the binomial 49x4
− 36y4
The difference of two terms with “square
coefficientsâ€and “even exponents†will always
be factored as the difference of squares.
49x4
− 36y4
49x4 − 36y4
(7x2 + 6y2)(7x2 − 6y2)
2. Factor the binomial x8
− y8
Sometimes the factors themselves contain
a factorable binomial
→ difference of squares.
Another difference of squares. Continue factoring:
Continue factoring to prime factors:
x8
− y8
x8 − y8 = (x4 + y4)(x4
− y4)
= (x4 + y4)(x2 + y2)(x2
− y2)
= (x4 + y4)(x2 + y2)(x +
y)(x − y)
3. Factor the expression (t + 4)2 − 9
Some expressions can be factored as the
“difference of squares†when one of the squared
terms is inside parentheses
Simplify:
(t + 4)2
− 9
[(t + 4) + 3][(t + 4) − 3]
(t + 7) (t + 1)
4.
Factor
Watch for fractions in the expressions.
5. Factor completely: 16x3y − 36xy3
Factor out the common factors then note that
the term in parentheses can be factored as
the difference of squares. The remaining
factors are “prime†in rational numbers.
