Answer
$q^{4} - 8q^{3} + 24q^{2} - 32q + 16$
Work Step by Step
1. Rewrite as product of binomials:
$(q - 2)^4$ = $(q-2)^2 \cdot (q-2)^2$
2. Squaring each we get :
$(q-2)^2 \cdot (q-2)^2 = (q^2 - 4q + 4) \cdot (q^2 - 4q + 4)$
3. Multiply these polynomials:
$(q^2 - 4q + 4) \cdot (q^2 - 4q + 4) = q^4 - 4q^3 + 4q^2 - 4q^3 +16q^2 - 16q + 4q^2 - 16q +16$
4. Combine like terms via addition/subtraction:
$q^4 - 4q^3 + 4q^2 - 4q^3 +16q^2 - 16q + 4q^2 - 16q +16 = q^{4} - 8q^{3} + 24q^{2} - 32q + 16$
The result is $q^{4} - 8q^{3} + 24q^{2} - 32q + 16$
