Factorise : 49a^2 + 70ab + 25b^2 - Vidyadip

Question

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

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Answer

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

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