Question

factor.
$64 + 27w^3$

Explanation:

Step1: Identify the sum of cubes

The expression \(64 + 27w^3\) can be written as \(4^3+(3w)^3\) since \(4^3 = 64\) and \((3w)^3=27w^3\).

Step2: Apply the sum of cubes formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(a = 4\) and \(b = 3w\).
Substitute \(a = 4\) and \(b = 3w\) into the formula:
\(a + b=4 + 3w\)
\(a^2=4^2 = 16\)
\(ab = 4\times(3w)=12w\)
\(b^2=(3w)^2 = 9w^2\)
So, \(a^2 - ab + b^2=16-12w + 9w^2\)
Thus, \(64 + 27w^3=(4 + 3w)(16-12w + 9w^2)\)

Answer:

\((4 + 3w)(9w^2-12w + 16)\)