Simplify ((a+b)^2)^2

${({(a + b)}^{2})}^{2}$

Step 1

Multiply the exponents in ${({(a + b)}^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(a + b)}^{2 \cdot 2}$

Multiply $2$ by $2$ .

${(a + b)}^{4}$

Step 2

Use the Binomial Theorem.

$a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4}$