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

1 Answer
May 6, 2016

Answer:

#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)|))#