Answer:
a² +3ab - 5ab - 15b² = (a+3b) (a-5b)
Step-by-step explanation:
We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,
[tex]a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)[/tex]
Now taking a common from the first two terms and 3b from last two terms, then :
[tex](a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)[/tex]
In the above expression, a factor (a-5b) is in both the terms. It would mean that,
[tex]a(a-5b)+3b(a-5b)=(a+3b)(a-5b)[/tex]
So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).
