Basic Math Examples

$(7 a^{2} - 12 y^{3}) (7 a^{2} + 12 y^{3})$

Step 1

Expand $(7 a^{2} - 12 y^{3}) (7 a^{2} + 12 y^{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 a^{2} (7 a^{2} + 12 y^{3}) - 12 y^{3} (7 a^{2} + 12 y^{3})$

Step 1.2

Apply the distributive property.

$7 a^{2} (7 a^{2}) + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2} + 12 y^{3})$

Step 1.3

Apply the distributive property.

$7 a^{2} (7 a^{2}) + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2

Simplify and combine like 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.

$7 \cdot 7 a^{2} a^{2} + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.2

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $a^{2}$ .

$7 \cdot 7 (a^{2} a^{2}) + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.2.2

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

$7 \cdot 7 a^{2 + 2} + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.2.3

Add $2$ and $2$ .

$7 \cdot 7 a^{4} + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.3

Multiply $7$ by $7$ .

$49 a^{4} + 7 a^{2} (12 y^{3}) - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$49 a^{4} + 7 \cdot 12 a^{2} y^{3} - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.5

Multiply $7$ by $12$ .

$49 a^{4} + 84 a^{2} y^{3} - 12 y^{3} (7 a^{2}) - 12 y^{3} (12 y^{3})$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$49 a^{4} + 84 a^{2} y^{3} - 12 \cdot 7 y^{3} a^{2} - 12 y^{3} (12 y^{3})$

Step 2.1.7

Multiply $- 12$ by $7$ .

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 12 y^{3} (12 y^{3})$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 12 \cdot 12 y^{3} y^{3}$

Step 2.1.9

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

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Step 2.1.9.1

Move $y^{3}$ .

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 12 \cdot 12 (y^{3} y^{3})$

Step 2.1.9.2

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

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 12 \cdot 12 y^{3 + 3}$

Step 2.1.9.3

Add $3$ and $3$ .

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 12 \cdot 12 y^{6}$

Step 2.1.10

Multiply $- 12$ by $12$ .

$49 a^{4} + 84 a^{2} y^{3} - 84 y^{3} a^{2} - 144 y^{6}$

Step 2.2

Subtract $84 y^{3} a^{2}$ from $84 a^{2} y^{3}$ .

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Step 2.2.1

Move $y^{3}$ .

$49 a^{4} + 84 a^{2} y^{3} - 84 a^{2} y^{3} - 144 y^{6}$

Step 2.2.2

Subtract $84 a^{2} y^{3}$ from $84 a^{2} y^{3}$ .

$49 a^{4} + 0 - 144 y^{6}$

Step 2.3

Add $49 a^{4}$ and $0$ .

$49 a^{4} - 144 y^{6}$