Question

find the product using special product formulas.
$(x - 5)(x + 5)\left(x^{2}-25\
ight)$
$(x - 5)(x + 5)\left(x^{2}-25\
ight)=\square$
(simplify your answer.)

Explanation:

Step1: Apply difference of squares

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

Step2: Rewrite original expression

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

Step3: Apply square of binomial

$(a-b)^2 = a^2 - 2ab + b^2$, so:
$(x^2)^2 - 2(x^2)(25) + 25^2 = x^4 - 50x^2 + 625$

Answer:

$x^4 - 50x^2 + 625$