Question

Factorize $25a^2-4b^2+28bc-49c^2$.

Answer 1

$25a^2-4b^2-28bc-49c^2$

$={\left(5a\right)}^2-{\left(2b\right)}^2+28bc-{\left(7c\right)}^2$

$={\left(5a\right)}^2-\left\{{\left(2b\right)}^2+2\times 2b\times 7c-{\left(7c\right)}^2\right\}$

$\because \left[{\left(a+b\right)}^2=a^2+b^2+2ab\right]$

$={\left(5a\right)}^2-{\left(2b+7c\right)}^2$

$\because \left[a^2-b^2=\left(a-b\right)\left(a+b\right)\right]$

$=\left\{\left(5a\right)-\left(2b+7c\right)\right\}\left\{\left(5a\right)+\left(2b+7c\right)\right\}$

$=\left(5a-2b-7c\right)\left(5a+2b+7c\right)$