Answer
$r^4 + 12r^3 + 54r^2 + 108r + 81$
Work Step by Step
1. Rewrite as product of binomials:
$(r + 3)^4 = (r + 3)^2 \cdot (r + 3)^2$
2. Square each:
$(r + 3)^2 \cdot (r + 3)^2 = (r^2 + 6r + 9) \cdot (r^2 + 6r + 9)$
3. Multiply the polynomials:
$(r^2 + 6r + 9) \cdot (r^2 + 6r + 9) = r^4 + 6r^3 + 9r^2 + 6r^3 + 36r^2 + 54r + 9r^2 + 54r + 81$
4. Combine like terms with addition:
$r^4 + 6r^3 + 9r^2 + 6r^3 + 36r^2 + 54r + 9r^2 + 54r + 81 = r^4 + 12r^3 + 54r^2 + 108r + 81$
The result is $r^4 + 12r^3 + 54r^2 + 108r + 81$
