could someone help me with like terms?

Question

Multiply and simplify

(a+1)(a-1)+(a-5)(a+5)

Answer 1

You have two pairs of conjugate pairs here.

 

(a+1)(a-1) = a² -a + a -1 = a² - 1

 

(a-5)(a+5) =a²-5a + 5a - 25 = a² - 25

 

So, you have

 

(a² - 1) + (a² - 25) = 2a² - 26

 

 

The pattern (a+b) (a-b) = a² - b²  is called the difference of two squares.  It is a very important formula, learn to recognize it.  It will save you a lot of trouble.