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

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Answer 1 · 2015-05-30T23:37:30

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

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

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

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

...using the difference of squares identity:

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

How do you factor x^2(25 - x^2)- 4(25 - x^2)x2(25−x2)−4(25−x2)x^2(25 - x^2)- 4(25 - x^2)?