Factorize the following:

Factorize the following:
28a2 + 14a2b2 − 21a4


The greatest common factor of the terms $28 a^{2}, 14 a^{2} b^{2}$ and $21 a^{4}$ of the expression $28 a^{2}+14 a^{2} b^{2}-21 a^{4}$ is $7 a^{2}$.

Also, we can write $28 a^{2}=7 a^{2} \times 4,14 a^{2} b^{2}=7 a^{2} \times 2 b^{2}$ and $21 a^{4}=7 a^{2} \times 3 a^{2}$.

$\therefore 28 a^{2}+14 a^{2} b^{2}-21 a^{4}=7 a^{2} \times 4+7 a^{2} \times 2 b^{2}-7 a^{2} \times 3 a^{2}$

$=7 a^{2}\left(4+2 b^{2}-3 a^{2}\right)$


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