how do i factor these equations

Question

Factor completely: w²  -4 How do i factor this equation

 

7s² -7d²

r³-12r²-144r+1728

 

 

Answer 1

w²-4=(w-2)(w+2)

 

7s²-7d²=7(s²-d²)=7(s-d)(s+d)

 

r³-12r²-144r+1728

Ordinarily you look at factors of the constant 1728, but I divided 1728 by 144 out of curiosity and got 12 !

This makes factoring this polynomial much easier.

(r³-12r²)+(-144r+1728)

r²(r-12)+(-144)(r-12)

(r-12)(r²-144)=(r-12)(r-12)(r+12)

these problems involve the difference of two squares:a²-b²=(a+b)(a-b)