Question

1. 128x³ + 250

Explanation:

Step1: Factor out the GCF

Find the greatest common factor of 128 and 250, which is 2.
$128x^3 + 250 = 2(64x^3 + 125)$

Step2: Recognize sum of cubes

$64x^3 = (4x)^3$ and $125 = 5^3$, use sum of cubes formula $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$.
$64x^3 + 125 = (4x)^3 + 5^3 = (4x + 5)((4x)^2 - (4x)(5) + 5^2)$

Step3: Simplify the quadratic term

Calculate each part of the quadratic factor.
$(4x)^2 - (4x)(5) + 5^2 = 16x^2 - 20x + 25$

Step4: Combine all factors

Substitute back into the expression from Step1.
$2(4x + 5)(16x^2 - 20x + 25)$

Answer:

$2(4x + 5)(16x^2 - 20x + 25)$