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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{5}$ .

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

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

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

Add $5$ and $5$ .

$3 \cdot 3 x^{10} + 3 x^{5} y^{4} + y^{4} (3 x^{5}) + y^{4} y^{4}$

Multiply $3$ by $3$ .

$9 x^{10} + 3 x^{5} y^{4} + y^{4} (3 x^{5}) + y^{4} y^{4}$

Rewrite using the commutative property of multiplication.

$9 x^{10} + 3 x^{5} y^{4} + 3 y^{4} x^{5} + y^{4} y^{4}$

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

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

$9 x^{10} + 3 x^{5} y^{4} + 3 y^{4} x^{5} + y^{4 + 4}$

Add $4$ and $4$ .

$9 x^{10} + 3 x^{5} y^{4} + 3 y^{4} x^{5} + y^{8}$

Add $3 x^{5} y^{4}$ and $3 y^{4} x^{5}$ .

Move $y^{4}$ .

$9 x^{10} + 3 x^{5} y^{4} + 3 x^{5} y^{4} + y^{8}$

Add $3 x^{5} y^{4}$ and $3 x^{5} y^{4}$ .

$9 x^{10} + 6 x^{5} y^{4} + y^{8}$