Question

1. ( k^3 - 27 )

Explanation:

Step1: Identify the formula

We use the difference of cubes formula: $a^3 - b^3=(a - b)(a^2+ab + b^2)$
Here, $a = k$ and $b = 3$ (since $3^3=27$)

Step2: Apply the formula

Substitute $a = k$ and $b = 3$ into the formula:
$k^3-27=k^3 - 3^3=(k - 3)(k^2+(k)(3)+3^2)$

Step3: Simplify the terms

Simplify the second factor:
$(k - 3)(k^2 + 3k+9)$

Answer:

$(k - 3)(k^2 + 3k + 9)$