Expand the product $(x-2)^2(x+2)^2$. What is the product of the nonzero coefficients of the resulting expressi

Question

Expand the product $(x-2)^2(x+2)^2$. What is the product of the nonzero coefficients of the resulting expression, including the constant term?

GPT-5 mini · Answer

(x-2)^2(x+2)^2 = [(x-2)(x+2)]^2 = (x^2 - 4)^2 = x^4 - 8x^2 + 16.

Nonzero coefficients are 1 (for x^4), -8 (for x^2), and 16 (constant). Their product is 1 * (-8) * 16 = -128.

Expand the product $(x-2)^2(x+2)^2$. What is the product of the nonzero coefficients of the resulting expression, including the constant term?