Question

How do you factor `x^2(25 - x^2)- 4(25 - x^2)`?

Answer 1

`x^2(25-x^2)-4(25-x^2)`

`=(x^2-4)(25-x^2)`

`=(x^2-2^2)(5^2-x^2)`

`=(x-2)(x+2)(5-x)(5+x)`

...using the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`