Find the Product (a^5-7b)^2

${(a^{5} - 7 b)}^{2}$

Rewrite ${(a^{5} - 7 b)}^{2}$ as $(a^{5} - 7 b) (a^{5} - 7 b)$ .

$(a^{5} - 7 b) (a^{5} - 7 b)$

Expand $(a^{5} - 7 b) (a^{5} - 7 b)$ using the FOIL Method.

Apply the distributive property.

$a^{5} (a^{5} - 7 b) - 7 b (a^{5} - 7 b)$

Apply the distributive property.

$a^{5} a^{5} + a^{5} (- 7 b) - 7 b (a^{5} - 7 b)$

Apply the distributive property.

$a^{5} a^{5} + a^{5} (- 7 b) - 7 b a^{5} - 7 b (- 7 b)$

Simplify and combine like terms.

Simplify each term.

Multiply $a^{5}$ by $a^{5}$ by adding the exponents.

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

$a^{5 + 5} + a^{5} (- 7 b) - 7 b a^{5} - 7 b (- 7 b)$

Add $5$ and $5$ .

$a^{10} + a^{5} (- 7 b) - 7 b a^{5} - 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$a^{10} - 7 a^{5} b - 7 b a^{5} - 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$a^{10} - 7 a^{5} b - 7 b a^{5} - 7 \cdot - 7 b \cdot b$

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

Move $b$ .

$a^{10} - 7 a^{5} b - 7 b a^{5} - 7 \cdot - 7 (b \cdot b)$

Multiply $b$ by $b$ .

$a^{10} - 7 a^{5} b - 7 b a^{5} - 7 \cdot - 7 b^{2}$

Multiply $- 7$ by $- 7$ .

$a^{10} - 7 a^{5} b - 7 b a^{5} + 49 b^{2}$

Subtract $7 b a^{5}$ from $- 7 a^{5} b$ .

Move $b$ .

$a^{10} - 7 a^{5} b - 7 a^{5} b + 49 b^{2}$

Subtract $7 a^{5} b$ from $- 7 a^{5} b$ .

$a^{10} - 14 a^{5} b + 49 b^{2}$