# How do you simplify 5.6x^2 (y^2 - z^2) - 3.5y^2 (x^2 - z^2) + 2.7x^2 (y^2 - z^2) + 4.8y^2 (x^2 - z^2)?

May 28, 2017

$8.3 {x}^{2} \left({y}^{2} - {z}^{2}\right) + 1.3 {y}^{2} \left({x}^{2} - {z}^{2}\right)$

#### Explanation:

Strategy: Combine terms with identical expressions and factor like crazy.

Step 1. Combine terms with identical expressions.

$5.6 \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} - 3.5 \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)} + 2.7 \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} + 4.8 \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)}$

$= 5.6 \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} + 2.7 \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} - 3.5 \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)} + 4.8 \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)}$

Step 2. Factor like crazy.

$= \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} \left(5.6 + 2.7\right) + \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)} \left(- 3.5 + 4.8\right)$

$= \textcolor{red}{{x}^{2} \left({y}^{2} - {z}^{2}\right)} 8.3 + \textcolor{b l u e}{{y}^{2} \left({x}^{2} - {z}^{2}\right)} 1.3$

$= 8.3 {x}^{2} \left({y}^{2} - {z}^{2}\right) + 1.3 {y}^{2} \left({x}^{2} - {z}^{2}\right)$