Question

Factorize `25x^2+60x+36`?

Answer 1

`25x^2+60x+36=(5x+6)^2`

Explanation:

In `25x^2+60x+36`, the first and third term are complete square as `25x^2=(5x)^2` and `36=6^2` and middle term is double the product of `5x` and `3` i.e. `2xx5x xx6=60x`

Hence using the identity `(a+b)^2=a^2+2ab+b^2`

`25x^2+60x+36`

= `(5x)^2+2xx5x xx6x+6^2`

= `(5x+6)^2`