Basic Math Examples

$- 8 a (3 a - 7) - 2 a (a + 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 8 a (3 a) - 8 a \cdot - 7 - 2 a (a + 5)$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 8 \cdot 3 a \cdot a - 8 a \cdot - 7 - 2 a (a + 5)$

Step 1.3

Multiply $- 7$ by $- 8$ .

$- 8 \cdot 3 a \cdot a + 56 a - 2 a (a + 5)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $a$ .

$- 8 \cdot 3 (a \cdot a) + 56 a - 2 a (a + 5)$

Step 1.4.1.2

Multiply $a$ by $a$ .

$- 8 \cdot 3 a^{2} + 56 a - 2 a (a + 5)$

Step 1.4.2

Multiply $- 8$ by $3$ .

$- 24 a^{2} + 56 a - 2 a (a + 5)$

Step 1.5

Apply the distributive property.

$- 24 a^{2} + 56 a - 2 a \cdot a - 2 a \cdot 5$

Step 1.6

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

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Step 1.6.1

Move $a$ .

$- 24 a^{2} + 56 a - 2 (a \cdot a) - 2 a \cdot 5$

Step 1.6.2

Multiply $a$ by $a$ .

$- 24 a^{2} + 56 a - 2 a^{2} - 2 a \cdot 5$

Step 1.7

Multiply $5$ by $- 2$ .

$- 24 a^{2} + 56 a - 2 a^{2} - 10 a$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 a^{2}$ from $- 24 a^{2}$ .

$- 26 a^{2} + 56 a - 10 a$

Step 2.2

Subtract $10 a$ from $56 a$ .

$- 26 a^{2} + 46 a$