Question:
Factorize the following:
20a12b2 − 15a8b4
Solution:
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 $5 a^{8} b^{2}$.
$20 a^{12} b^{2}=5 \times 4 \times a^{8} \times a^{4} \times b^{2}=5 a^{8} \times b^{2} \times 4 a^{4}$ 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 20a12b2 - 15a8b4 can be factorised as 5a8b2(4a4-3b2)