Simplify (a^2-2b)^2

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

Step 1

Rewrite ${(a^{2} - 2 b)}^{2}$ as $(a^{2} - 2 b) (a^{2} - 2 b)$ .

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

Step 2

Expand $(a^{2} - 2 b) (a^{2} - 2 b)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

$a^{4} + a^{2} (- 2 b) - 2 b a^{2} - 2 b (- 2 b)$

Rewrite using the commutative property of multiplication.

$a^{4} - 2 a^{2} b - 2 b a^{2} - 2 b (- 2 b)$

Rewrite using the commutative property of multiplication.

$a^{4} - 2 a^{2} b - 2 b a^{2} - 2 \cdot - 2 b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$a^{4} - 2 a^{2} b - 2 b a^{2} - 2 \cdot - 2 (b \cdot b)$

Multiply $b$ by $b$ .

$a^{4} - 2 a^{2} b - 2 b a^{2} - 2 \cdot - 2 b^{2}$

Multiply $- 2$ by $- 2$ .

$a^{4} - 2 a^{2} b - 2 b a^{2} + 4 b^{2}$

Subtract $2 b a^{2}$ from $- 2 a^{2} b$ .

Move $b$ .

$a^{4} - 2 a^{2} b - 2 a^{2} b + 4 b^{2}$

Subtract $2 a^{2} b$ from $- 2 a^{2} b$ .

$a^{4} - 4 a^{2} b + 4 b^{2}$