Simplify (4x^4-y^4)^2

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

Step 1

Rewrite ${(4 x^{4} - y^{4})}^{2}$ as $(4 x^{4} - y^{4}) (4 x^{4} - y^{4})$ .

$(4 x^{4} - y^{4}) (4 x^{4} - y^{4})$

Step 2

Expand $(4 x^{4} - y^{4}) (4 x^{4} - y^{4})$ using the FOIL Method.

Apply the distributive property.

$4 x^{4} (4 x^{4} - y^{4}) - y^{4} (4 x^{4} - y^{4})$

Apply the distributive property.

$4 x^{4} (4 x^{4}) + 4 x^{4} (- y^{4}) - y^{4} (4 x^{4} - y^{4})$

Apply the distributive property.

$4 x^{4} (4 x^{4}) + 4 x^{4} (- y^{4}) - y^{4} (4 x^{4}) - y^{4} (- y^{4})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{4}$ .

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

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

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

Add $4$ and $4$ .

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

Multiply $4$ by $4$ .

$16 x^{8} + 4 x^{4} (- y^{4}) - y^{4} (4 x^{4}) - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$16 x^{8} + 4 \cdot - 1 x^{4} y^{4} - y^{4} (4 x^{4}) - y^{4} (- y^{4})$

Multiply $4$ by $- 1$ .

$16 x^{8} - 4 x^{4} y^{4} - y^{4} (4 x^{4}) - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$16 x^{8} - 4 x^{4} y^{4} - 1 \cdot 4 y^{4} x^{4} - y^{4} (- y^{4})$

Multiply $- 1$ by $4$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} - 1 \cdot - 1 y^{4} y^{4}$

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

Move $y^{4}$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} - 1 \cdot - 1 (y^{4} y^{4})$

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

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} - 1 \cdot - 1 y^{4 + 4}$

Add $4$ and $4$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} - 1 \cdot - 1 y^{8}$

Multiply $- 1$ by $- 1$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} + 1 y^{8}$

Multiply $y^{8}$ by $1$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 y^{4} x^{4} + y^{8}$

Subtract $4 y^{4} x^{4}$ from $- 4 x^{4} y^{4}$ .

Move $y^{4}$ .

$16 x^{8} - 4 x^{4} y^{4} - 4 x^{4} y^{4} + y^{8}$

Subtract $4 x^{4} y^{4}$ from $- 4 x^{4} y^{4}$ .

$16 x^{8} - 8 x^{4} y^{4} + y^{8}$

Simplify (4x^4-y^4)^2

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