Simplify (8w^4+w^3)^2

${(8 w^{4} + w^{3})}^{2}$

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

$(8 w^{4} + w^{3}) (8 w^{4} + w^{3})$

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

Apply the distributive property.

$8 w^{4} (8 w^{4} + w^{3}) + w^{3} (8 w^{4} + w^{3})$

Apply the distributive property.

$8 w^{4} (8 w^{4}) + 8 w^{4} w^{3} + w^{3} (8 w^{4} + w^{3})$

Apply the distributive property.

$8 w^{4} (8 w^{4}) + 8 w^{4} w^{3} + w^{3} (8 w^{4}) + w^{3} w^{3}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $w^{4}$ .

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

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

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

Add $4$ and $4$ .

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

Multiply $8$ by $8$ .

$64 w^{8} + 8 w^{4} w^{3} + w^{3} (8 w^{4}) + w^{3} w^{3}$

Multiply $w^{4}$ by $w^{3}$ by adding the exponents.

Move $w^{3}$ .

$64 w^{8} + 8 (w^{3} w^{4}) + w^{3} (8 w^{4}) + w^{3} w^{3}$

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

$64 w^{8} + 8 w^{3 + 4} + w^{3} (8 w^{4}) + w^{3} w^{3}$

Add $3$ and $4$ .

$64 w^{8} + 8 w^{7} + w^{3} (8 w^{4}) + w^{3} w^{3}$

Rewrite using the commutative property of multiplication.

$64 w^{8} + 8 w^{7} + 8 w^{3} w^{4} + w^{3} w^{3}$

Multiply $w^{3}$ by $w^{4}$ by adding the exponents.

Move $w^{4}$ .

$64 w^{8} + 8 w^{7} + 8 (w^{4} w^{3}) + w^{3} w^{3}$

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

$64 w^{8} + 8 w^{7} + 8 w^{4 + 3} + w^{3} w^{3}$

Add $4$ and $3$ .

$64 w^{8} + 8 w^{7} + 8 w^{7} + w^{3} w^{3}$

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

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

$64 w^{8} + 8 w^{7} + 8 w^{7} + w^{3 + 3}$

Add $3$ and $3$ .

$64 w^{8} + 8 w^{7} + 8 w^{7} + w^{6}$

Add $8 w^{7}$ and $8 w^{7}$ .

$64 w^{8} + 16 w^{7} + w^{6}$

Simplify (8w^4+w^3)^2

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