Write as a product

Question

Write as a product

ab^2 –a–b^3+b

Write as a productab² –a–b³+b

Answer 1

Here we're going to try and group the numbers and see what we can factor out.  Starting with the first two terms, we can pull out a

ab²-a = a(b²-1)

and for the second two terms, we can pull out b (or -b)

-b³+b = -b(b²-1)

Then write the equation together:

a(b²-1)-b(b²-1)

and you notice that both a and -b are multiplied by (b²-1).  From there, we can rewrite the equation as

(a-b)*(b²-1)

which is a product.  Tada!