Simplify (6mn^4+3m^5p)^2

${(6 m n^{4} + 3 m^{5} p)}^{2}$

Rewrite ${(6 m n^{4} + 3 m^{5} p)}^{2}$ as $(6 m n^{4} + 3 m^{5} p) (6 m n^{4} + 3 m^{5} p)$ .

$(6 m n^{4} + 3 m^{5} p) (6 m n^{4} + 3 m^{5} p)$

Expand $(6 m n^{4} + 3 m^{5} p) (6 m n^{4} + 3 m^{5} p)$ using the FOIL Method.

Apply the distributive property.

$6 m n^{4} (6 m n^{4} + 3 m^{5} p) + 3 m^{5} p (6 m n^{4} + 3 m^{5} p)$

Apply the distributive property.

$6 m n^{4} (6 m n^{4}) + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4} + 3 m^{5} p)$

Apply the distributive property.

$6 m n^{4} (6 m n^{4}) + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Simplify and combine like terms.

Simplify each term.

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$6 (m \cdot m) n^{4} (6 n^{4}) + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $m$ by $m$ .

$6 m^{2} n^{4} (6 n^{4}) + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

Move $n^{4}$ .

$6 m^{2} (n^{4} n^{4}) \cdot 6 + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

$6 m^{2} n^{4 + 4} \cdot 6 + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Add $4$ and $4$ .

$6 m^{2} n^{8} \cdot 6 + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $6$ by $6$ .

$36 m^{2} n^{8} + 6 m n^{4} (3 m^{5} p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

Move $m^{5}$ .

$36 m^{2} n^{8} + 6 (m^{5} m) n^{4} (3 p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $m^{5}$ by $m$ .

Raise $m$ to the power of $1$ .

$36 m^{2} n^{8} + 6 (m^{5} m^{1}) n^{4} (3 p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

$36 m^{2} n^{8} + 6 m^{5 + 1} n^{4} (3 p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Add $5$ and $1$ .

$36 m^{2} n^{8} + 6 m^{6} n^{4} (3 p) + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $3$ by $6$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 3 m^{5} p (6 m n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

Move $m$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 3 (m \cdot m^{5}) p (6 n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $m$ by $m^{5}$ .

Raise $m$ to the power of $1$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 3 (m^{1} m^{5}) p (6 n^{4}) + 3 m^{5} p (3 m^{5} p)$

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

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 3 m^{1 + 5} p (6 n^{4}) + 3 m^{5} p (3 m^{5} p)$

Add $1$ and $5$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 3 m^{6} p (6 n^{4}) + 3 m^{5} p (3 m^{5} p)$

Multiply $6$ by $3$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 m^{5} p (3 m^{5} p)$

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

Move $m^{5}$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 (m^{5} m^{5}) p (3 p)$

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

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 m^{5 + 5} p (3 p)$

Add $5$ and $5$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 m^{10} p (3 p)$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 m^{10} (p \cdot p) \cdot 3$

Multiply $p$ by $p$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 3 m^{10} p^{2} \cdot 3$

Multiply $3$ by $3$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} p n^{4} + 9 m^{10} p^{2}$

Add $18 m^{6} n^{4} p$ and $18 m^{6} p n^{4}$ .

Move $p$ .

$36 m^{2} n^{8} + 18 m^{6} n^{4} p + 18 m^{6} n^{4} p + 9 m^{10} p^{2}$

Add $18 m^{6} n^{4} p$ and $18 m^{6} n^{4} p$ .

$36 m^{2} n^{8} + 36 m^{6} n^{4} p + 9 m^{10} p^{2}$

Simplify (6mn^4+3m^5p)^2

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