Basic Math Examples

$(9 a^{2} - 25 b^{2}) (9 a^{2} + 25 y^{2})$

Step 1

Expand $(9 a^{2} - 25 b^{2}) (9 a^{2} + 25 y^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 a^{2} (9 a^{2} + 25 y^{2}) - 25 b^{2} (9 a^{2} + 25 y^{2})$

Step 1.2

Apply the distributive property.

$9 a^{2} (9 a^{2}) + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2} + 25 y^{2})$

Step 1.3

Apply the distributive property.

$9 a^{2} (9 a^{2}) + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$9 \cdot 9 a^{2} a^{2} + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.2

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

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Step 2.2.1

Move $a^{2}$ .

$9 \cdot 9 (a^{2} a^{2}) + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.2.2

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

$9 \cdot 9 a^{2 + 2} + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.2.3

Add $2$ and $2$ .

$9 \cdot 9 a^{4} + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.3

Multiply $9$ by $9$ .

$81 a^{4} + 9 a^{2} (25 y^{2}) - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.4

Rewrite using the commutative property of multiplication.

$81 a^{4} + 9 \cdot 25 a^{2} y^{2} - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.5

Multiply $9$ by $25$ .

$81 a^{4} + 225 a^{2} y^{2} - 25 b^{2} (9 a^{2}) - 25 b^{2} (25 y^{2})$

Step 2.6

Rewrite using the commutative property of multiplication.

$81 a^{4} + 225 a^{2} y^{2} - 25 \cdot 9 b^{2} a^{2} - 25 b^{2} (25 y^{2})$

Step 2.7

Multiply $- 25$ by $9$ .

$81 a^{4} + 225 a^{2} y^{2} - 225 b^{2} a^{2} - 25 b^{2} (25 y^{2})$

Step 2.8

Rewrite using the commutative property of multiplication.

$81 a^{4} + 225 a^{2} y^{2} - 225 b^{2} a^{2} - 25 \cdot 25 b^{2} y^{2}$

Step 2.9

Multiply $- 25$ by $25$ .

$81 a^{4} + 225 a^{2} y^{2} - 225 b^{2} a^{2} - 625 b^{2} y^{2}$