How would i multiply and simplify to the lowest terms ?

Question

(t+7)^2/t+2 * (t +2)^2/t+7=?

(Simplify answer in factored form.)

Answer 1

(t+7)^2/t+2 * (t +2)^2/t+7    Rewrite it

(t+7) (t+7) * (t+2)(t+2) / ((t+2) *(t+7))  Simplyfy by canceling top and bottom with common terms

(t+7)(t+2)            answer in factored form (nothing left on bottom)

Answer 2

The easiest way to multiply this would first be to see what the numerator and denominator have in common.  In this case, the denominator has a (t+2)(t+7), where the numerator has (t+7)(t+7)(t+2)(t+2).  Once we've established this, we notice you can eliminate a (t+2) and a (t+7) from both the top and bottom, leaving us with (t+7)(t+2).  If the answer needs to be FOILed, you end up with t^2+9t+14.