I need help simplifying the polynomial (t-5)^2 (t+5)^2

Question

I'm really struggling with the steps and applying the formula (A-B)^2=A^2-2AB+B^2 

I'd really appreciate any help I can get but please show the work so I can learn from it.

I seem to loose my negatives and/or exponents and I'm very frustrated. 

Answer 1

First, we expand the expression.

 

(t - 5)(t - 5)(t + 5)(t + 5)

 

 

If we rearrange the factors, we can get 2 differences of perfect squares.

 

(t - 5)(t + 5) * (t - 5)(t + 5) =

 

(t² - 25) * (t² - 25) =

 

t⁴ - 50t² + 625

 

 

Answer 2

This expression is more easily understood if you separate the factors.

 

(t - 5)² (t + 5)²

when rewritten, this expression becomes (t + 5)(t -5)(t + 5)(t + 5)

when we expand the first part, we get t² -10t + 25

when we expand the second par, we get t² + 10t + 25

 

when we multiply these two expressions, we get t⁴ - 100t² + 50t² + 625

 

combining, we get t⁴ - 50t² + 625