Factor completely x3x225125x225Solutionx3x2 25 125 x2 25 T

Factor completely:

x^3(x^2-25)-125(x^2-25)

x^3(x^2 - 25) -125 ( x^2 -25)

Taking out ( x^2 -25)

(x^2 -25) ( x^3 -125)

(x^2 -25) ( x^3 -5^3)

Using formula (a^3 - b^3) =( a-b)(a^2 +ab +b^2)

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

(x^2 -25)( x- 5)(x^2 +5x +25)

( x-5)(x+5)( x-5)(x^2 +5x +25)

So, x^3(x^2 - 25) -125 ( x^2 -25) = (x-5)^2(x+5)(x^2 +5x +25