Question

1. $x^{3}+125=$

Explanation:

Step1: Recognize sum of cubes

Note that $125 = 5^3$, so $x^3 + 125 = x^3 + 5^3$. Use the sum of cubes formula: $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$.

Step2: Substitute values into formula

Let $a=x$, $b=5$. Substitute into the formula:
$x^3 + 5^3 = (x+5)(x^2 - x\cdot5 + 5^2)$

Step3: Simplify the second factor

Calculate the terms in the quadratic factor:
$(x+5)(x^2 - 5x + 25)$

Answer:

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