Basic Math Examples

$6 a (a^{2} + 5 a - 4) + 9 a (- 2 a^{2} + a)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$6 a \cdot a^{2} + 6 a (5 a) + 6 a \cdot - 4 + 9 a (- 2 a^{2} + a)$

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

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

Tap for more steps...

Step 1.2.1.1

Move $a^{2}$ .

$6 (a^{2} a) + 6 a (5 a) + 6 a \cdot - 4 + 9 a (- 2 a^{2} + a)$

Step 1.2.1.2

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

Tap for more steps...

Step 1.2.1.2.1

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

$6 (a^{2} a^{1}) + 6 a (5 a) + 6 a \cdot - 4 + 9 a (- 2 a^{2} + a)$

Step 1.2.1.2.2

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

$6 a^{2 + 1} + 6 a (5 a) + 6 a \cdot - 4 + 9 a (- 2 a^{2} + a)$

Step 1.2.1.3

Add $2$ and $1$ .

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.2.3

Multiply $- 4$ by $6$ .

$6 a^{3} + 6 \cdot 5 a \cdot a - 24 a + 9 a (- 2 a^{2} + a)$

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

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

Tap for more steps...

Step 1.3.1.1

Move $a$ .

$6 a^{3} + 6 \cdot 5 (a \cdot a) - 24 a + 9 a (- 2 a^{2} + a)$

Step 1.3.1.2

Multiply $a$ by $a$ .

$6 a^{3} + 6 \cdot 5 a^{2} - 24 a + 9 a (- 2 a^{2} + a)$

Step 1.3.2

Multiply $6$ by $5$ .

$6 a^{3} + 30 a^{2} - 24 a + 9 a (- 2 a^{2} + a)$

Step 1.4

Apply the distributive property.

$6 a^{3} + 30 a^{2} - 24 a + 9 a (- 2 a^{2}) + 9 a \cdot a$

Step 1.5

Rewrite using the commutative property of multiplication.

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 a \cdot a^{2} + 9 a \cdot a$

Step 1.6

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

Tap for more steps...

Step 1.6.1

Move $a$ .

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 a \cdot a^{2} + 9 (a \cdot a)$

Step 1.6.2

Multiply $a$ by $a$ .

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 a \cdot a^{2} + 9 a^{2}$

Step 1.7

Simplify each term.

Tap for more steps...

Step 1.7.1

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

Tap for more steps...

Step 1.7.1.1

Move $a^{2}$ .

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 (a^{2} a) + 9 a^{2}$

Step 1.7.1.2

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

Tap for more steps...

Step 1.7.1.2.1

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

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 (a^{2} a^{1}) + 9 a^{2}$

Step 1.7.1.2.2

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

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 a^{2 + 1} + 9 a^{2}$

Step 1.7.1.3

Add $2$ and $1$ .

$6 a^{3} + 30 a^{2} - 24 a + 9 \cdot - 2 a^{3} + 9 a^{2}$

Step 1.7.2

Multiply $9$ by $- 2$ .

$6 a^{3} + 30 a^{2} - 24 a - 18 a^{3} + 9 a^{2}$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $18 a^{3}$ from $6 a^{3}$ .

$- 12 a^{3} + 30 a^{2} - 24 a + 9 a^{2}$

Step 2.2

Add $30 a^{2}$ and $9 a^{2}$ .

$- 12 a^{3} + 39 a^{2} - 24 a$