Basic Math Examples

$(5 a + 3 b) (5 a - 3 b) (25 a^{2} + 9 b^{2})$

Step 1

Expand $(5 a + 3 b) (5 a - 3 b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(5 a (5 a - 3 b) + 3 b (5 a - 3 b)) (25 a^{2} + 9 b^{2})$

Step 1.2

Apply the distributive property.

$(5 a (5 a) + 5 a (- 3 b) + 3 b (5 a - 3 b)) (25 a^{2} + 9 b^{2})$

Step 1.3

Apply the distributive property.

$(5 a (5 a) + 5 a (- 3 b) + 3 b (5 a) + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $5 a (5 a) + 5 a (- 3 b) + 3 b (5 a) + 3 b (- 3 b)$ .

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Step 2.1.1

Reorder the factors in the terms $5 a (- 3 b)$ and $3 b (5 a)$ .

$(5 a (5 a) - 3 \cdot 5 a b + 3 \cdot 5 a b + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.1.2

Add $- 3 \cdot 5 a b$ and $3 \cdot 5 a b$ .

$(5 a (5 a) + 0 + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.1.3

Add $5 a (5 a)$ and $0$ .

$(5 a (5 a) + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$(5 \cdot 5 a \cdot a + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.2.2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.2.2.1

Move $a$ .

$(5 \cdot 5 (a \cdot a) + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.2.2.2

Multiply $a$ by $a$ .

$(5 \cdot 5 a^{2} + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.2.3

Multiply $5$ by $5$ .

$(25 a^{2} + 3 b (- 3 b)) (25 a^{2} + 9 b^{2})$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$(25 a^{2} + 3 \cdot - 3 b \cdot b) (25 a^{2} + 9 b^{2})$

Step 2.2.5

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.5.1

Move $b$ .

$(25 a^{2} + 3 \cdot - 3 (b \cdot b)) (25 a^{2} + 9 b^{2})$

Step 2.2.5.2

Multiply $b$ by $b$ .

$(25 a^{2} + 3 \cdot - 3 b^{2}) (25 a^{2} + 9 b^{2})$

Step 2.2.6

Multiply $3$ by $- 3$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify terms.

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Step 4.1

Combine the opposite terms in $25 a^{2} (25 a^{2}) + 25 a^{2} (9 b^{2}) - 9 b^{2} (25 a^{2}) - 9 b^{2} (9 b^{2})$ .

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Step 4.1.1

Reorder the factors in the terms $25 a^{2} (9 b^{2})$ and $- 9 b^{2} (25 a^{2})$ .

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

Step 4.1.2

Subtract $9 \cdot 25 a^{2} b^{2}$ from $9 \cdot 25 a^{2} b^{2}$ .

$25 a^{2} (25 a^{2}) + 0 - 9 b^{2} (9 b^{2})$

Step 4.1.3

Add $25 a^{2} (25 a^{2})$ and $0$ .

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

Step 4.2

Simplify each term.

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Step 4.2.1

Rewrite using the commutative property of multiplication.

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

Step 4.2.2

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

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Step 4.2.2.1

Move $a^{2}$ .

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

Step 4.2.2.2

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

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

Step 4.2.2.3

Add $2$ and $2$ .

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

Step 4.2.3

Multiply $25$ by $25$ .

$625 a^{4} - 9 b^{2} (9 b^{2})$

Step 4.2.4

Rewrite using the commutative property of multiplication.

$625 a^{4} - 9 \cdot 9 b^{2} b^{2}$

Step 4.2.5

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

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Step 4.2.5.1

Move $b^{2}$ .

$625 a^{4} - 9 \cdot 9 (b^{2} b^{2})$

Step 4.2.5.2

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

$625 a^{4} - 9 \cdot 9 b^{2 + 2}$

Step 4.2.5.3

Add $2$ and $2$ .

$625 a^{4} - 9 \cdot 9 b^{4}$

Step 4.2.6

Multiply $- 9$ by $9$ .

$625 a^{4} - 81 b^{4}$