Q 173. - Intermediate Algebra

Question

In the following exercises, factor completely using the perfect square trinomial pattern.

$75u^4-30u^{3}v+3u^2{v}^2$

Step-by-Step Solution

Answer

The factor of the given trinomial is  $3u^2{\left(5u-v\right)}^2$.

Step 1. Given information.

Consider the given trinomial.

$75u^4-30u^{3}v+3u^2{v}^2$

Step 2. Factor out GCF

Factor out $3u^2$ from the given trinomial.

$3u^2\left(25u^2-10uv+v^2\right)$

Step 3. Find the factor of perfect square trinomial.

The middle term of the trinomial is negative, so the binomial square will be of the form ${\left(a-b\right)}^2$.

$3u^2\left[{\left(5u\right)}^2-2·5u·v+{\left(v\right)}^2\right]$

Write factor

$3u^2{\left(5u-v\right)}^2$