Question

. Factorize a² +3ab - 5ab - 15b²

Answer 1

a² +3ab - 5ab - 15b² = (a+3b) (a-5b)

Explanation:

We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,

`a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)`

Now taking a common from the first two terms and 3b from last two terms, then :

`(a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)`

In the above expression, a factor (a-5b) is in both the terms. It would mean that,

`a(a-5b)+3b(a-5b)=(a+3b)(a-5b)`

So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).