Pre-Algebra Examples

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

Step 1

Expand $(3 x^{4} - y^{2}) (5 x^{2} + y^{4})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $x^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $4$ .

$3 \cdot 5 x^{6} + 3 x^{4} y^{4} - y^{2} (5 x^{2}) - y^{2} y^{4}$

Step 2.1.3

Multiply $3$ by $5$ .

$15 x^{6} + 3 x^{4} y^{4} - y^{2} (5 x^{2}) - y^{2} y^{4}$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$15 x^{6} + 3 x^{4} y^{4} - 1 \cdot 5 y^{2} x^{2} - y^{2} y^{4}$

Step 2.1.5

Multiply $- 1$ by $5$ .

$15 x^{6} + 3 x^{4} y^{4} - 5 y^{2} x^{2} - y^{2} y^{4}$

Step 2.1.6

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

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Step 2.1.6.1

Move $y^{4}$ .

$15 x^{6} + 3 x^{4} y^{4} - 5 y^{2} x^{2} - (y^{4} y^{2})$

Step 2.1.6.2

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

$15 x^{6} + 3 x^{4} y^{4} - 5 y^{2} x^{2} - y^{4 + 2}$

Step 2.1.6.3

Add $4$ and $2$ .

$15 x^{6} + 3 x^{4} y^{4} - 5 y^{2} x^{2} - y^{6}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $y^{2}$ .

$15 x^{6} + 3 x^{4} y^{4} - 5 x^{2} y^{2} - y^{6}$

Step 2.2.2

Move $- 5 x^{2} y^{2}$ .

$15 x^{6} + 3 x^{4} y^{4} - y^{6} - 5 x^{2} y^{2}$

Step 2.2.3

Reorder $15 x^{6}$ and $3 x^{4} y^{4}$ .

$3 x^{4} y^{4} + 15 x^{6} - y^{6} - 5 x^{2} y^{2}$