Simplify (4m^5+5n^6)^2

${(4 m^{5} + 5 n^{6})}^{2}$

Rewrite ${(4 m^{5} + 5 n^{6})}^{2}$ as $(4 m^{5} + 5 n^{6}) (4 m^{5} + 5 n^{6})$ .

$(4 m^{5} + 5 n^{6}) (4 m^{5} + 5 n^{6})$

Expand $(4 m^{5} + 5 n^{6}) (4 m^{5} + 5 n^{6})$ using the FOIL Method.

Apply the distributive property.

$4 m^{5} (4 m^{5} + 5 n^{6}) + 5 n^{6} (4 m^{5} + 5 n^{6})$

Apply the distributive property.

$4 m^{5} (4 m^{5}) + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5} + 5 n^{6})$

Apply the distributive property.

$4 m^{5} (4 m^{5}) + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 m^{5} m^{5} + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

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

Move $m^{5}$ .

$4 \cdot 4 (m^{5} m^{5}) + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

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

$4 \cdot 4 m^{5 + 5} + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Add $5$ and $5$ .

$4 \cdot 4 m^{10} + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Multiply $4$ by $4$ .

$16 m^{10} + 4 m^{5} (5 n^{6}) + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Rewrite using the commutative property of multiplication.

$16 m^{10} + 4 \cdot 5 m^{5} n^{6} + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Multiply $4$ by $5$ .

$16 m^{10} + 20 m^{5} n^{6} + 5 n^{6} (4 m^{5}) + 5 n^{6} (5 n^{6})$

Rewrite using the commutative property of multiplication.

$16 m^{10} + 20 m^{5} n^{6} + 5 \cdot 4 n^{6} m^{5} + 5 n^{6} (5 n^{6})$

Multiply $5$ by $4$ .

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 5 n^{6} (5 n^{6})$

Rewrite using the commutative property of multiplication.

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 5 \cdot 5 n^{6} n^{6}$

Multiply $n^{6}$ by $n^{6}$ by adding the exponents.

Move $n^{6}$ .

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 5 \cdot 5 (n^{6} n^{6})$

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

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 5 \cdot 5 n^{6 + 6}$

Add $6$ and $6$ .

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 5 \cdot 5 n^{12}$

Multiply $5$ by $5$ .

$16 m^{10} + 20 m^{5} n^{6} + 20 n^{6} m^{5} + 25 n^{12}$

Add $20 m^{5} n^{6}$ and $20 n^{6} m^{5}$ .

Move $n^{6}$ .

$16 m^{10} + 20 m^{5} n^{6} + 20 m^{5} n^{6} + 25 n^{12}$

Add $20 m^{5} n^{6}$ and $20 m^{5} n^{6}$ .

$16 m^{10} + 40 m^{5} n^{6} + 25 n^{12}$

Move $16 m^{10}$ .

$40 m^{5} n^{6} + 25 n^{12} + 16 m^{10}$

Reorder $40 m^{5} n^{6}$ and $25 n^{12}$ .

$25 n^{12} + 40 m^{5} n^{6} + 16 m^{10}$

Simplify (4m^5+5n^6)^2

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