Question
Factorize the following expressions : $\frac{1}{2} y^2-8 z^2$
✓
Answer
\begin{aligned}
\frac{1}{2} y^2-8 z^2 \\
& =\frac{1}{2} y^2-\frac{2 \times 8}{2} z^2 \\
& =\frac{1}{2} y^2-\frac{1}{2} \times 16 z^2 \\
& =\frac{1}{2}\left(y^2-16 z^2\right)=\frac{1}{2}\left[y^2-(4 z)^2\right] \\
& =\frac{1}{2}[(y+4 z)(y-4 z)]
\end{aligned}
\frac{1}{2} y^2-8 z^2 \\
& =\frac{1}{2} y^2-\frac{2 \times 8}{2} z^2 \\
& =\frac{1}{2} y^2-\frac{1}{2} \times 16 z^2 \\
& =\frac{1}{2}\left(y^2-16 z^2\right)=\frac{1}{2}\left[y^2-(4 z)^2\right] \\
& =\frac{1}{2}[(y+4 z)(y-4 z)]
\end{aligned}
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