Question

Factor Differences of Squares

In the following exercises, factor.

$49u^3-9u$

Short answer

The factors for$49u^3-9u=u(7u+3)(7u-3)$

Step-by-step solution

Step 1. Given information

The given differences of squares$49u^3-9u$

Step 2. Finding the factors for given differences of squares

Take uas common from the given differences of squares as follows $49u^3-9u=u(49u^2-9)$

We can find the factors as follows

Use the sum product pattern

$u(49u^2-9)=u(49u^2-21u+21u-9)$

Common factors from the two pairs

$u\left(7u\right(7u-3)+3(7u-3\left)\right)$

Rewrite in factored form

$u(7u+3)(7u-3)$

Therefore,the factors for$49u^3-9u=u(7u+3)(7u-3)$