Question

Factorize this equation

Answer 1

Hey There!!

Here we will use the identity :

$x^2-2xy+y^2=(x-y)^2$


Now, coming to your question:

$(a+b)^2-14c(a+b)+49c^2 \\ \\ =(a+b)^2 - 2(a+b)(7c) + (7c)^2 \\ \\ =((a+b)-7c)^2 \\ \\ = (a+b-7c)^2$

Here, we just noticed that the first and last terms were perfect squares.

And the middle term also was given so that we could use the identity.

Thus, we finally have the answer:

$\boxed{(a+b)^2-14c(a+b)+49c^2=(a+b-7c)^2}$


Hope it helps
Purva
Brainly Community

Answer 2

(a+b)^2-14c(a+b)+49c^2
=(a+b)^2-2*(a+b)*7c+(7c)^2
=(a+b-7c)^2