Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $b^{6}$ by $b^{3}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $b^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $6$ .

$- 3 b^{9} c \cdot 4 - 3 b^{6} c (- 5 b^{4} c^{2 + 7 c^{2}})$

Step 3

Multiply $b^{6}$ by $b^{4}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $b^{4}$ .

$- 3 b^{9} c \cdot 4 - 3 (b^{4} b^{6}) c (- 5 c^{2 + 7 c^{2}})$

Step 3.2

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

$- 3 b^{9} c \cdot 4 - 3 b^{4 + 6} c (- 5 c^{2 + 7 c^{2}})$

Step 3.3

Add $4$ and $6$ .

$- 3 b^{9} c \cdot 4 - 3 b^{10} c (- 5 c^{2 + 7 c^{2}})$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $4$ by $- 3$ .

$- 12 b^{9} c - 3 b^{10} c (- 5 c^{2 + 7 c^{2}})$

Step 4.2

Multiply $c$ by $c^{2 + 7 c^{2}}$ by adding the exponents.

Tap for more steps...

Step 4.2.1

Move $c^{2 + 7 c^{2}}$ .

$- 12 b^{9} c - 3 b^{10} (c^{2 + 7 c^{2}} c) \cdot - 5$

Step 4.2.2

Multiply $c^{2 + 7 c^{2}}$ by $c$ .

Tap for more steps...

Step 4.2.2.1

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

$- 12 b^{9} c - 3 b^{10} (c^{2 + 7 c^{2}} c^{1}) \cdot - 5$

Step 4.2.2.2

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

$- 12 b^{9} c - 3 b^{10} c^{2 + 7 c^{2} + 1} \cdot - 5$

Step 4.2.3

Add $2$ and $1$ .

$- 12 b^{9} c - 3 b^{10} c^{7 c^{2} + 3} \cdot - 5$

Step 4.3

Multiply $- 5$ by $- 3$ .

$- 12 b^{9} c + 15 b^{10} c^{7 c^{2} + 3}$