Finite Math Examples

$7 a^{7} (5 a - 6) - (5 a - 6)$

Step 1

Apply the distributive property.

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

Multiply $- 6$ by $7$ .

$7 \cdot 5 a^{7} a - 42 a^{7} - (5 a - 6)$

Step 4

Simplify each term.

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Step 4.1

Multiply $a^{7}$ by $a$ by adding the exponents.

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Step 4.1.1

Move $a$ .

$7 \cdot 5 (a \cdot a^{7}) - 42 a^{7} - (5 a - 6)$

Step 4.1.2

Multiply $a$ by $a^{7}$ .

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Step 4.1.2.1

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

$7 \cdot 5 (a^{1} a^{7}) - 42 a^{7} - (5 a - 6)$

Step 4.1.2.2

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

$7 \cdot 5 a^{1 + 7} - 42 a^{7} - (5 a - 6)$

Step 4.1.3

Add $1$ and $7$ .

$7 \cdot 5 a^{8} - 42 a^{7} - (5 a - 6)$

Step 4.2

Multiply $7$ by $5$ .

$35 a^{8} - 42 a^{7} - (5 a - 6)$

Step 5

Apply the distributive property.

$35 a^{8} - 42 a^{7} - (5 a) - - 6$

Step 6

Multiply $5$ by $- 1$ .

$35 a^{8} - 42 a^{7} - 5 a - - 6$

Step 7

Multiply $- 1$ by $- 6$ .

$35 a^{8} - 42 a^{7} - 5 a + 6$