Algebra Examples

$2 a^{2} (5 a - 6) - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 a^{2} (5 a) + 2 a^{2} \cdot - 6 - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.2

Rewrite using the commutative property of multiplication.

$2 \cdot 5 a^{2} a + 2 a^{2} \cdot - 6 - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.3

Multiply $- 6$ by $2$ .

$2 \cdot 5 a^{2} a - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $a$ .

$2 \cdot 5 (a \cdot a^{2}) - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$2 \cdot 5 (a^{1} a^{2}) - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.4.1.2.2

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

$2 \cdot 5 a^{1 + 2} - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.4.1.3

Add $1$ and $2$ .

$2 \cdot 5 a^{3} - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.4.2

Multiply $2$ by $5$ .

$10 a^{3} - 12 a^{2} - 5 a (a^{2} - 3 a + 4) - 7 (a - 5)$

Step 1.5

Apply the distributive property.

$10 a^{3} - 12 a^{2} - 5 a \cdot a^{2} - 5 a (- 3 a) - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6

Simplify.

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Step 1.6.1

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

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Step 1.6.1.1

Move $a^{2}$ .

$10 a^{3} - 12 a^{2} - 5 (a^{2} a) - 5 a (- 3 a) - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6.1.2

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

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Step 1.6.1.2.1

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

$10 a^{3} - 12 a^{2} - 5 (a^{2} a^{1}) - 5 a (- 3 a) - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6.1.2.2

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

$10 a^{3} - 12 a^{2} - 5 a^{2 + 1} - 5 a (- 3 a) - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6.1.3

Add $2$ and $1$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} - 5 a (- 3 a) - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$10 a^{3} - 12 a^{2} - 5 a^{3} - 5 \cdot - 3 a \cdot a - 5 a \cdot 4 - 7 (a - 5)$

Step 1.6.3

Multiply $4$ by $- 5$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} - 5 \cdot - 3 a \cdot a - 20 a - 7 (a - 5)$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $a$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} - 5 \cdot - 3 (a \cdot a) - 20 a - 7 (a - 5)$

Step 1.7.1.2

Multiply $a$ by $a$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} - 5 \cdot - 3 a^{2} - 20 a - 7 (a - 5)$

Step 1.7.2

Multiply $- 5$ by $- 3$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} + 15 a^{2} - 20 a - 7 (a - 5)$

Step 1.8

Apply the distributive property.

$10 a^{3} - 12 a^{2} - 5 a^{3} + 15 a^{2} - 20 a - 7 a - 7 \cdot - 5$

Step 1.9

Multiply $- 7$ by $- 5$ .

$10 a^{3} - 12 a^{2} - 5 a^{3} + 15 a^{2} - 20 a - 7 a + 35$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 a^{3}$ from $10 a^{3}$ .

$5 a^{3} - 12 a^{2} + 15 a^{2} - 20 a - 7 a + 35$

Step 2.2

Add $- 12 a^{2}$ and $15 a^{2}$ .

$5 a^{3} + 3 a^{2} - 20 a - 7 a + 35$

Step 2.3

Subtract $7 a$ from $- 20 a$ .

$5 a^{3} + 3 a^{2} - 27 a + 35$