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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{5}$ .

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

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

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

Add $5$ and $5$ .

$2 \cdot 2 x^{10} + 2 x^{5} (- y^{5}) - y^{5} (2 x^{5}) - y^{5} (- y^{5})$

Multiply $2$ by $2$ .

$4 x^{10} + 2 x^{5} (- y^{5}) - y^{5} (2 x^{5}) - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

$4 x^{10} + 2 \cdot - 1 x^{5} y^{5} - y^{5} (2 x^{5}) - y^{5} (- y^{5})$

Multiply $2$ by $- 1$ .

$4 x^{10} - 2 x^{5} y^{5} - y^{5} (2 x^{5}) - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

$4 x^{10} - 2 x^{5} y^{5} - 1 \cdot 2 y^{5} x^{5} - y^{5} (- y^{5})$

Multiply $- 1$ by $2$ .

$4 x^{10} - 2 x^{5} y^{5} - 2 y^{5} x^{5} - y^{5} (- y^{5})$

Rewrite using the commutative property of multiplication.

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

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

Move $y^{5}$ .

$4 x^{10} - 2 x^{5} y^{5} - 2 y^{5} x^{5} - 1 \cdot - 1 (y^{5} y^{5})$

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

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

Add $5$ and $5$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

Move $y^{5}$ .

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

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

$4 x^{10} - 4 x^{5} y^{5} + y^{10}$

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

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