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Factorization — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorization2 Marks
Question
Factorize:
$20 a^{12} b^2-15 a^8 b^4$
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Answer

The greatest common factor of the terms
$20 a^{12} b^2$ and $-15 a^8 b^4$ of the expression $20 a^{12} b^2-15 a^8 b^4$ is $5 a^8 b^2$.
$20 a^{12} b^2=5 \times 4 \times a^8 \times a^4 \times b^2=5 a^8 \times b^2 \times 4 a^4 \text { and }-15 a^8 b^4=5 \times-3 \times a^8 \times b^2 \times b^2=5 a^8 b^2 \times(-3) b^2$
Hence, the expression $20 a^{12} b^2-15 a^8 b^4$ can be factorised as $5 a^8 b^2\left(4 a^4-3 b^2\right)$

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