### Home > INT3 > Chapter 9 > Lesson 9.1.5 > Problem9-69

9-69.

Factor each of the following expressions. Look for the difference of squares and common factors.

1. $4 x ^ { 2 } - 9 y ^ { 2 }$

Remember the rule $\left(a + b\right)\left(a − b\right) = \left(a^{2} − b^{2}\right)$.

$\left(2x + 3y\right)\left(2x − 3y\right)$

1. $8 x ^ { 3 } - 2 x ^ { 7 }$

Remember to remove common factors.

$2x^{3}\left(4 − x^{4}\right)$

$2x^{3}\left(2 − x^{2}\right)\left(2+ x^{2}\right)$

1. $x ^ { 4 } - 81 y ^ { 4 }$

See part (a).

1. $8 x ^ { 3 } + 2 x ^ { 7 }$

See part (b).

1. Did you use any factoring pattern to factor the expressions? If so, describe them. If not, what pattern do you see in these expressions? How can you use that pattern to factor quickly?

The pattern for parts (a) through (c) is that they contain a difference of squares.