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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{4}$ .

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

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

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

Add $4$ and $4$ .

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

Multiply $5$ by $5$ .

$25 x^{8} + 5 x^{4} (- y^{3}) - y^{3} (5 x^{4}) - y^{3} (- y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{8} + 5 \cdot - 1 x^{4} y^{3} - y^{3} (5 x^{4}) - y^{3} (- y^{3})$

Multiply $5$ by $- 1$ .

$25 x^{8} - 5 x^{4} y^{3} - y^{3} (5 x^{4}) - y^{3} (- y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{8} - 5 x^{4} y^{3} - 1 \cdot 5 y^{3} x^{4} - y^{3} (- y^{3})$

Multiply $- 1$ by $5$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} - y^{3} (- y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} - 1 \cdot - 1 y^{3} y^{3}$

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

Move $y^{3}$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} - 1 \cdot - 1 (y^{3} y^{3})$

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

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} - 1 \cdot - 1 y^{3 + 3}$

Add $3$ and $3$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} - 1 \cdot - 1 y^{6}$

Multiply $- 1$ by $- 1$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} + 1 y^{6}$

Multiply $y^{6}$ by $1$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 y^{3} x^{4} + y^{6}$

Subtract $5 y^{3} x^{4}$ from $- 5 x^{4} y^{3}$ .

Move $y^{3}$ .

$25 x^{8} - 5 x^{4} y^{3} - 5 x^{4} y^{3} + y^{6}$

Subtract $5 x^{4} y^{3}$ from $- 5 x^{4} y^{3}$ .

$25 x^{8} - 10 x^{4} y^{3} + y^{6}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.