Simplify (2x^3-y^4)^2

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

Step 1

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

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

Step 2

Expand $(2 x^{3} - y^{4}) (2 x^{3} - y^{4})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

$2 \cdot 2 x^{6} + 2 x^{3} (- y^{4}) - y^{4} (2 x^{3}) - y^{4} (- y^{4})$

Multiply $2$ by $2$ .

$4 x^{6} + 2 x^{3} (- y^{4}) - y^{4} (2 x^{3}) - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$4 x^{6} + 2 \cdot - 1 x^{3} y^{4} - y^{4} (2 x^{3}) - y^{4} (- y^{4})$

Multiply $2$ by $- 1$ .

$4 x^{6} - 2 x^{3} y^{4} - y^{4} (2 x^{3}) - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$4 x^{6} - 2 x^{3} y^{4} - 1 \cdot 2 y^{4} x^{3} - y^{4} (- y^{4})$

Multiply $- 1$ by $2$ .

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} - y^{4} (- y^{4})$

Rewrite using the commutative property of multiplication.

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} - 1 \cdot - 1 y^{4} y^{4}$

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

Move $y^{4}$ .

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} - 1 \cdot - 1 (y^{4} y^{4})$

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

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} - 1 \cdot - 1 y^{4 + 4}$

Add $4$ and $4$ .

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} - 1 \cdot - 1 y^{8}$

Multiply $- 1$ by $- 1$ .

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} + 1 y^{8}$

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

$4 x^{6} - 2 x^{3} y^{4} - 2 y^{4} x^{3} + y^{8}$

Subtract $2 y^{4} x^{3}$ from $- 2 x^{3} y^{4}$ .

Move $y^{4}$ .

$4 x^{6} - 2 x^{3} y^{4} - 2 x^{3} y^{4} + y^{8}$

Subtract $2 x^{3} y^{4}$ from $- 2 x^{3} y^{4}$ .

$4 x^{6} - 4 x^{3} y^{4} + y^{8}$

Step 4

Move $4 x^{6}$ .

$- 4 x^{3} y^{4} + y^{8} + 4 x^{6}$

Step 5

Reorder $- 4 x^{3} y^{4}$ and $y^{8}$ .

$y^{8} - 4 x^{3} y^{4} + 4 x^{6}$

Simplify (2x^3-y^4)^2

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