Question
Evaluate the following using identities: $\big(1.5\text{x}^2-0.3\text{y}^2\big)\big(1.5\text{x}+0.3\text{y}^2\big)$
✓
Answer
We have, $\big(1.5\text{x}^2-0.3\text{y}^2\big)\big(1.5\text{x}+0.3\text{y}^2\big)$
$=\big[1.5\text{x}^2\big]^2-\big[0.3\text{y}^2\big]^2$
$\begin{bmatrix}\because(\text{a}+\text{b})(\text{a}-\text{b})=\text{a}^2-\text{b}^2$
$\text{a}=1.5\text{x}^2\ \text{and}\ \text{b}=0.3\text{y}^2\end{bmatrix}$
$=2.25\text{x}^4-0.09\text{y}^4$
$=\big[1.5\text{x}^2-0.3\text{y}^2\big]\big[1.5\text{x}^2+0.3\text{y}^2\big]$
$=2.25\text{x}^4-0.09\text{y}^4.$
$=\big[1.5\text{x}^2\big]^2-\big[0.3\text{y}^2\big]^2$
$\begin{bmatrix}\because(\text{a}+\text{b})(\text{a}-\text{b})=\text{a}^2-\text{b}^2$
$\text{a}=1.5\text{x}^2\ \text{and}\ \text{b}=0.3\text{y}^2\end{bmatrix}$
$=2.25\text{x}^4-0.09\text{y}^4$
$=\big[1.5\text{x}^2-0.3\text{y}^2\big]\big[1.5\text{x}^2+0.3\text{y}^2\big]$
$=2.25\text{x}^4-0.09\text{y}^4.$
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