Question
Factorise : $49 a^2+70 a b+25 b^2$
✓
Answer
Here you can see that $49 a^2=(7 a)^2, 25 b^2=(5 b)^2, 70 a b=2(7 a)(5 b)$
Comparing with $x^2+2 x y+y^2$, we observe that $x=7 a$ and $y=5 b$.
Using Identity $(x+y)^2=x^2+2 x y+y$, we get
$49 a^2+70 a b+25 b^2=(7 a+5 b)^2=(7 a+5 b)(7 a+5 b)$
This is the required factorisation.
Comparing with $x^2+2 x y+y^2$, we observe that $x=7 a$ and $y=5 b$.
Using Identity $(x+y)^2=x^2+2 x y+y$, we get
$49 a^2+70 a b+25 b^2=(7 a+5 b)^2=(7 a+5 b)(7 a+5 b)$
This is the required factorisation.
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