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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{4}$ .

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

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

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

Add $4$ and $4$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

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

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

Add $5$ and $5$ .

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

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

Move $y^{5}$ .

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

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

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

Step 4

Move $9 x^{8}$ .

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

Step 5

Reorder $6 x^{4} y^{5}$ and $y^{10}$ .

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