Simplify (3a^4-5b^2)^2

${(3 a^{4} - 5 b^{2})}^{2}$

Step 1

Rewrite ${(3 a^{4} - 5 b^{2})}^{2}$ as $(3 a^{4} - 5 b^{2}) (3 a^{4} - 5 b^{2})$ .

$(3 a^{4} - 5 b^{2}) (3 a^{4} - 5 b^{2})$

Step 2

Expand $(3 a^{4} - 5 b^{2}) (3 a^{4} - 5 b^{2})$ using the FOIL Method.

Apply the distributive property.

$3 a^{4} (3 a^{4} - 5 b^{2}) - 5 b^{2} (3 a^{4} - 5 b^{2})$

Apply the distributive property.

$3 a^{4} (3 a^{4}) + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4} - 5 b^{2})$

Apply the distributive property.

$3 a^{4} (3 a^{4}) + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 a^{4} a^{4} + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Multiply $a^{4}$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$3 \cdot 3 (a^{4} a^{4}) + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

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

$3 \cdot 3 a^{4 + 4} + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Add $4$ and $4$ .

$3 \cdot 3 a^{8} + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Multiply $3$ by $3$ .

$9 a^{8} + 3 a^{4} (- 5 b^{2}) - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Rewrite using the commutative property of multiplication.

$9 a^{8} + 3 \cdot - 5 a^{4} b^{2} - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Multiply $3$ by $- 5$ .

$9 a^{8} - 15 a^{4} b^{2} - 5 b^{2} (3 a^{4}) - 5 b^{2} (- 5 b^{2})$

Rewrite using the commutative property of multiplication.

$9 a^{8} - 15 a^{4} b^{2} - 5 \cdot 3 b^{2} a^{4} - 5 b^{2} (- 5 b^{2})$

Multiply $- 5$ by $3$ .

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} - 5 b^{2} (- 5 b^{2})$

Rewrite using the commutative property of multiplication.

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} - 5 \cdot - 5 b^{2} b^{2}$

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

Move $b^{2}$ .

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} - 5 \cdot - 5 (b^{2} b^{2})$

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

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} - 5 \cdot - 5 b^{2 + 2}$

Add $2$ and $2$ .

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} - 5 \cdot - 5 b^{4}$

Multiply $- 5$ by $- 5$ .

$9 a^{8} - 15 a^{4} b^{2} - 15 b^{2} a^{4} + 25 b^{4}$

Subtract $15 b^{2} a^{4}$ from $- 15 a^{4} b^{2}$ .

Move $b^{2}$ .

$9 a^{8} - 15 a^{4} b^{2} - 15 a^{4} b^{2} + 25 b^{4}$

Subtract $15 a^{4} b^{2}$ from $- 15 a^{4} b^{2}$ .

$9 a^{8} - 30 a^{4} b^{2} + 25 b^{4}$

Simplify (3a^4-5b^2)^2

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