Simplify (2x^3+4x^5)^2

${(2 x^{3} + 4 x^{5})}^{2}$

Rewrite ${(2 x^{3} + 4 x^{5})}^{2}$ as $(2 x^{3} + 4 x^{5}) (2 x^{3} + 4 x^{5})$ .

$(2 x^{3} + 4 x^{5}) (2 x^{3} + 4 x^{5})$

Expand $(2 x^{3} + 4 x^{5}) (2 x^{3} + 4 x^{5})$ using the FOIL Method.

Apply the distributive property.

$2 x^{3} (2 x^{3} + 4 x^{5}) + 4 x^{5} (2 x^{3} + 4 x^{5})$

Apply the distributive property.

$2 x^{3} (2 x^{3}) + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3} + 4 x^{5})$

Apply the distributive property.

$2 x^{3} (2 x^{3}) + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x^{3} x^{3} + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

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

Move $x^{3}$ .

$2 \cdot 2 (x^{3} x^{3}) + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

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

$2 \cdot 2 x^{3 + 3} + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Add $3$ and $3$ .

$2 \cdot 2 x^{6} + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Multiply $2$ by $2$ .

$4 x^{6} + 2 x^{3} (4 x^{5}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Rewrite using the commutative property of multiplication.

$4 x^{6} + 2 \cdot 4 x^{3} x^{5} + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$4 x^{6} + 2 \cdot 4 (x^{5} x^{3}) + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

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

$4 x^{6} + 2 \cdot 4 x^{5 + 3} + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Add $5$ and $3$ .

$4 x^{6} + 2 \cdot 4 x^{8} + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Multiply $2$ by $4$ .

$4 x^{6} + 8 x^{8} + 4 x^{5} (2 x^{3}) + 4 x^{5} (4 x^{5})$

Rewrite using the commutative property of multiplication.

$4 x^{6} + 8 x^{8} + 4 \cdot 2 x^{5} x^{3} + 4 x^{5} (4 x^{5})$

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$4 x^{6} + 8 x^{8} + 4 \cdot 2 (x^{3} x^{5}) + 4 x^{5} (4 x^{5})$

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

$4 x^{6} + 8 x^{8} + 4 \cdot 2 x^{3 + 5} + 4 x^{5} (4 x^{5})$

Add $3$ and $5$ .

$4 x^{6} + 8 x^{8} + 4 \cdot 2 x^{8} + 4 x^{5} (4 x^{5})$

Multiply $4$ by $2$ .

$4 x^{6} + 8 x^{8} + 8 x^{8} + 4 x^{5} (4 x^{5})$

Rewrite using the commutative property of multiplication.

$4 x^{6} + 8 x^{8} + 8 x^{8} + 4 \cdot 4 x^{5} x^{5}$

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

Move $x^{5}$ .

$4 x^{6} + 8 x^{8} + 8 x^{8} + 4 \cdot 4 (x^{5} x^{5})$

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

$4 x^{6} + 8 x^{8} + 8 x^{8} + 4 \cdot 4 x^{5 + 5}$

Add $5$ and $5$ .

$4 x^{6} + 8 x^{8} + 8 x^{8} + 4 \cdot 4 x^{10}$

Multiply $4$ by $4$ .

$4 x^{6} + 8 x^{8} + 8 x^{8} + 16 x^{10}$

Add $8 x^{8}$ and $8 x^{8}$ .

$4 x^{6} + 16 x^{8} + 16 x^{10}$

Simplify (2x^3+4x^5)^2

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