Question

Using appropriate identity, factorise the following:-
(1)$49a^2+70ab+25b^2$
(2)$9a^2-30ab+25b^2$

Answer 1

We have,

Part $\left(1\right)$

$49a^2+70ab+25b^2$

$\Rightarrow (7a{)}^2+2\times 7a\times 5b+(5b{)}^2$

$\Rightarrow (7a+5b{)}^2$ $\because (a+b{)}^2=a^2+b^2+2ab$

Part $\left(2\right)$

$9a^2-30ab+25b^2$

$\Rightarrow (3a{)}^2-2\times 3a\times 5b+(5b{)}^2$

$\Rightarrow (3a-5b{)}^2$ $\because (a-b{)}^2=a^2+b^2-2ab$

Hence, this is the answer.