Basic Math Examples

$(4 a - 6) (5 a^{2} - 5 a - 5)$

Step 1

Expand $(4 a - 6) (5 a^{2} - 5 a - 5)$ by multiplying each term in the first expression by each term in the second expression.

$4 a (5 a^{2}) + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

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.

$4 \cdot 5 a \cdot a^{2} + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.2

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

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Step 2.1.2.1

Move $a^{2}$ .

$4 \cdot 5 (a^{2} a) + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$4 \cdot 5 (a^{2} a^{1}) + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.2.2.2

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

$4 \cdot 5 a^{2 + 1} + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.2.3

Add $2$ and $1$ .

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

Step 2.1.3

Multiply $4$ by $5$ .

$20 a^{3} + 4 a (- 5 a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$20 a^{3} + 4 \cdot - 5 a \cdot a + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.5

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

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Step 2.1.5.1

Move $a$ .

$20 a^{3} + 4 \cdot - 5 (a \cdot a) + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.5.2

Multiply $a$ by $a$ .

$20 a^{3} + 4 \cdot - 5 a^{2} + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.6

Multiply $4$ by $- 5$ .

$20 a^{3} - 20 a^{2} + 4 a \cdot - 5 - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.7

Multiply $- 5$ by $4$ .

$20 a^{3} - 20 a^{2} - 20 a - 6 (5 a^{2}) - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.8

Multiply $5$ by $- 6$ .

$20 a^{3} - 20 a^{2} - 20 a - 30 a^{2} - 6 (- 5 a) - 6 \cdot - 5$

Step 2.1.9

Multiply $- 5$ by $- 6$ .

$20 a^{3} - 20 a^{2} - 20 a - 30 a^{2} + 30 a - 6 \cdot - 5$

Step 2.1.10

Multiply $- 6$ by $- 5$ .

$20 a^{3} - 20 a^{2} - 20 a - 30 a^{2} + 30 a + 30$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $30 a^{2}$ from $- 20 a^{2}$ .

$20 a^{3} - 50 a^{2} - 20 a + 30 a + 30$

Step 2.2.2

Add $- 20 a$ and $30 a$ .

$20 a^{3} - 50 a^{2} + 10 a + 30$