Finite Math Examples

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

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

Step 1

Apply the distributive property.

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

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

Step 2

Rewrite using the commutative property of multiplication.

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

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

Step 3

Multiply

- 6

$- 6$ by

7

$7$ .

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

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply

a^{7}

$a^{7}$ by

a

$a$ by adding the exponents.

Tap for more steps...

Step 4.1.1

Move

a

$a$ .

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

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

Step 4.1.2

Multiply

a

$a$ by

a^{7}

$a^{7}$ .

Tap for more steps...

Step 4.1.2.1

Raise

a

$a$ to the power of

1

$1$ .

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

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

Step 4.1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 4.1.3

Add

1

$1$ and

7

$7$ .

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

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

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

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

Step 4.2

Multiply

7

$7$ by

5

$5$ .

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

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

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

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

Step 5

Apply the distributive property.

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

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

Step 6

Multiply

5

$5$ by

- 1

$- 1$ .

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

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

Step 7

Multiply

- 1

$- 1$ by

- 6

$- 6$ .

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

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