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

Question

1724 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-30T23:37:30

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

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

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

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

...using the difference of squares identity:

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

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