Simplify (3x^2-y^5)^2

${(3 x^{2} - y^{5})}^{2}$

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

$(3 x^{2} - y^{5}) (3 x^{2} - y^{5})$

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

Apply the distributive property.

$3 x^{2} (3 x^{2} - y^{5}) - y^{5} (3 x^{2} - y^{5})$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $3$ .

$9 x^{4} + 3 x^{2} (- y^{5}) - y^{5} (3 x^{2}) - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

$9 x^{4} + 3 \cdot - 1 x^{2} y^{5} - y^{5} (3 x^{2}) - y^{5} (- y^{5})$

Multiply $3$ by $- 1$ .

$9 x^{4} - 3 x^{2} y^{5} - y^{5} (3 x^{2}) - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

$9 x^{4} - 3 x^{2} y^{5} - 1 \cdot 3 y^{5} x^{2} - y^{5} (- y^{5})$

Multiply $- 1$ by $3$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} - 1 \cdot - 1 y^{5} y^{5}$

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

Move $y^{5}$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} - 1 \cdot - 1 (y^{5} y^{5})$

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

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} - 1 \cdot - 1 y^{5 + 5}$

Add $5$ and $5$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} - 1 \cdot - 1 y^{10}$

Multiply $- 1$ by $- 1$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} + 1 y^{10}$

Multiply $y^{10}$ by $1$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 y^{5} x^{2} + y^{10}$

Subtract $3 y^{5} x^{2}$ from $- 3 x^{2} y^{5}$ .

Move $y^{5}$ .

$9 x^{4} - 3 x^{2} y^{5} - 3 x^{2} y^{5} + y^{10}$

Subtract $3 x^{2} y^{5}$ from $- 3 x^{2} y^{5}$ .

$9 x^{4} - 6 x^{2} y^{5} + y^{10}$

Move $9 x^{4}$ .

$- 6 x^{2} y^{5} + y^{10} + 9 x^{4}$

Reorder $- 6 x^{2} y^{5}$ and $y^{10}$ .

$y^{10} - 6 x^{2} y^{5} + 9 x^{4}$

Simplify (3x^2-y^5)^2

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