Find the Product (3a^3+8b^4)^2

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

Step 1

Rewrite ${(3 a^{3} + 8 b^{4})}^{2}$ as $(3 a^{3} + 8 b^{4}) (3 a^{3} + 8 b^{4})$ .

$(3 a^{3} + 8 b^{4}) (3 a^{3} + 8 b^{4})$

Step 2

Expand $(3 a^{3} + 8 b^{4}) (3 a^{3} + 8 b^{4})$ using the FOIL Method.

Apply the distributive property.

$3 a^{3} (3 a^{3} + 8 b^{4}) + 8 b^{4} (3 a^{3} + 8 b^{4})$

Apply the distributive property.

$3 a^{3} (3 a^{3}) + 3 a^{3} (8 b^{4}) + 8 b^{4} (3 a^{3} + 8 b^{4})$

Apply the distributive property.

$3 a^{3} (3 a^{3}) + 3 a^{3} (8 b^{4}) + 8 b^{4} (3 a^{3}) + 8 b^{4} (8 b^{4})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $a^{3}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

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

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

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

Add $3$ and $3$ .

$3 \cdot 3 a^{6} + 3 a^{3} (8 b^{4}) + 8 b^{4} (3 a^{3}) + 8 b^{4} (8 b^{4})$

Multiply $3$ by $3$ .

$9 a^{6} + 3 a^{3} (8 b^{4}) + 8 b^{4} (3 a^{3}) + 8 b^{4} (8 b^{4})$

Rewrite using the commutative property of multiplication.

$9 a^{6} + 3 \cdot 8 a^{3} b^{4} + 8 b^{4} (3 a^{3}) + 8 b^{4} (8 b^{4})$

Multiply $3$ by $8$ .

$9 a^{6} + 24 a^{3} b^{4} + 8 b^{4} (3 a^{3}) + 8 b^{4} (8 b^{4})$

Rewrite using the commutative property of multiplication.

$9 a^{6} + 24 a^{3} b^{4} + 8 \cdot 3 b^{4} a^{3} + 8 b^{4} (8 b^{4})$

Multiply $8$ by $3$ .

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 8 b^{4} (8 b^{4})$

Rewrite using the commutative property of multiplication.

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 8 \cdot 8 b^{4} b^{4}$

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

Move $b^{4}$ .

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 8 \cdot 8 (b^{4} b^{4})$

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

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 8 \cdot 8 b^{4 + 4}$

Add $4$ and $4$ .

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 8 \cdot 8 b^{8}$

Multiply $8$ by $8$ .

$9 a^{6} + 24 a^{3} b^{4} + 24 b^{4} a^{3} + 64 b^{8}$

Add $24 a^{3} b^{4}$ and $24 b^{4} a^{3}$ .

Move $b^{4}$ .

$9 a^{6} + 24 a^{3} b^{4} + 24 a^{3} b^{4} + 64 b^{8}$

Add $24 a^{3} b^{4}$ and $24 a^{3} b^{4}$ .

$9 a^{6} + 48 a^{3} b^{4} + 64 b^{8}$

Find the Product (3a^3+8b^4)^2

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