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

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

Step 1

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

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

Step 2

Expand $(7 b^{5} - b^{2}) (7 b^{5} - b^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 7 b^{5} b^{5} + 7 b^{5} (- b^{2}) - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

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

Move $b^{5}$ .

$7 \cdot 7 (b^{5} b^{5}) + 7 b^{5} (- b^{2}) - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

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

$7 \cdot 7 b^{5 + 5} + 7 b^{5} (- b^{2}) - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Add $5$ and $5$ .

$7 \cdot 7 b^{10} + 7 b^{5} (- b^{2}) - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Multiply $7$ by $7$ .

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

Rewrite using the commutative property of multiplication.

$49 b^{10} + 7 \cdot - 1 b^{5} b^{2} - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Multiply $b^{5}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$49 b^{10} + 7 \cdot - 1 (b^{2} b^{5}) - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

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

$49 b^{10} + 7 \cdot - 1 b^{2 + 5} - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Add $2$ and $5$ .

$49 b^{10} + 7 \cdot - 1 b^{7} - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Multiply $7$ by $- 1$ .

$49 b^{10} - 7 b^{7} - b^{2} (7 b^{5}) - b^{2} (- b^{2})$

Rewrite using the commutative property of multiplication.

$49 b^{10} - 7 b^{7} - 1 \cdot 7 b^{2} b^{5} - b^{2} (- b^{2})$

Multiply $b^{2}$ by $b^{5}$ by adding the exponents.

Move $b^{5}$ .

$49 b^{10} - 7 b^{7} - 1 \cdot 7 (b^{5} b^{2}) - b^{2} (- b^{2})$

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

$49 b^{10} - 7 b^{7} - 1 \cdot 7 b^{5 + 2} - b^{2} (- b^{2})$

Add $5$ and $2$ .

$49 b^{10} - 7 b^{7} - 1 \cdot 7 b^{7} - b^{2} (- b^{2})$

Multiply $- 1$ by $7$ .

$49 b^{10} - 7 b^{7} - 7 b^{7} - b^{2} (- b^{2})$

Rewrite using the commutative property of multiplication.

$49 b^{10} - 7 b^{7} - 7 b^{7} - 1 \cdot - 1 b^{2} b^{2}$

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

Move $b^{2}$ .

$49 b^{10} - 7 b^{7} - 7 b^{7} - 1 \cdot - 1 (b^{2} b^{2})$

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

$49 b^{10} - 7 b^{7} - 7 b^{7} - 1 \cdot - 1 b^{2 + 2}$

Add $2$ and $2$ .

$49 b^{10} - 7 b^{7} - 7 b^{7} - 1 \cdot - 1 b^{4}$

Multiply $- 1$ by $- 1$ .

$49 b^{10} - 7 b^{7} - 7 b^{7} + 1 b^{4}$

Multiply $b^{4}$ by $1$ .

$49 b^{10} - 7 b^{7} - 7 b^{7} + b^{4}$

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

$49 b^{10} - 14 b^{7} + b^{4}$

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

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