Question

How do you factor `a^3b^3-16ab^3`?

Answer 1

`ab^3(a-4)(a+4)`

Explanation:

Looking for common factors in the 2 terms.

from `a^3" and a we get " a`

from `b^3 and" b^3→ b^3`

`rArra^3b^3-16ab^3=ab^3(a^2-16)`

now `a^2-16" is a" color(blue)" difference of squares"`

and in general factorises as `a^2-b^2=(a-b)(a+b)`

For `a^2-16 , a=a " and " b=4→ (a-4)(a+4)`

`rArrcolor(red)(|bar(ul(color(white)(a/a)color(black)(a^3b^3-16ab^3=ab^3(a-4)(a+4))color(white)(a/a)|))`