Basic Math Examples

$(2 a - 5) (a^{2} - 1)$

Step 1

Expand $(2 a - 5) (a^{2} - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 a (a^{2} - 1) - 5 (a^{2} - 1)$

Step 1.2

Apply the distributive property.

$2 a \cdot a^{2} + 2 a \cdot - 1 - 5 (a^{2} - 1)$

Step 1.3

Apply the distributive property.

$2 a \cdot a^{2} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $a^{2}$ .

$2 (a^{2} a) + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Step 2.1.1.2

Multiply $a^{2}$ by $a$ .

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Step 2.1.1.2.1

Raise $a$ to the power of $1$ .

$2 (a^{2} a^{1}) + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Step 2.1.1.2.2

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

$2 a^{2 + 1} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Step 2.1.1.3

Add $2$ and $1$ .

$2 a^{3} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Step 2.1.2

Multiply $- 1$ by $2$ .

$2 a^{3} - 2 a - 5 a^{2} - 5 \cdot - 1$

Step 2.1.3

Multiply $- 5$ by $- 1$ .

$2 a^{3} - 2 a - 5 a^{2} + 5$

Step 2.2

Move $- 2 a$ .

$2 a^{3} - 5 a^{2} - 2 a + 5$