Basic Math Examples

$(2 a^{2} - b) (- 3 a + 2 b)$

Step 1

Expand $(2 a^{2} - b) (- 3 a + 2 b)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$2 a^{2} (- 3 a + 2 b) - b (- 3 a + 2 b)$

Step 1.2

Apply the distributive property.

$2 a^{2} (- 3 a) + 2 a^{2} (2 b) - b (- 3 a + 2 b)$

Step 1.3

Apply the distributive property.

$2 a^{2} (- 3 a) + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot - 3 a^{2} a + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $a$ .

$2 \cdot - 3 (a \cdot a^{2}) + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.2.2

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

Tap for more steps...

Step 2.1.2.2.1

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

$2 \cdot - 3 (a^{1} a^{2}) + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.2.2.2

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

$2 \cdot - 3 a^{1 + 2} + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.2.3

Add $1$ and $2$ .

$2 \cdot - 3 a^{3} + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.3

Multiply $2$ by $- 3$ .

$- 6 a^{3} + 2 a^{2} (2 b) - b (- 3 a) - b (2 b)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$- 6 a^{3} + 2 \cdot 2 a^{2} b - b (- 3 a) - b (2 b)$

Step 2.1.5

Multiply $2$ by $2$ .

$- 6 a^{3} + 4 a^{2} b - b (- 3 a) - b (2 b)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$- 6 a^{3} + 4 a^{2} b - 1 \cdot - 3 b a - b (2 b)$

Step 2.1.7

Multiply $- 1$ by $- 3$ .

$- 6 a^{3} + 4 a^{2} b + 3 b a - b (2 b)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$- 6 a^{3} + 4 a^{2} b + 3 b a - 1 \cdot 2 b \cdot b$

Step 2.1.9

Multiply $b$ by $b$ by adding the exponents.

Tap for more steps...

Step 2.1.9.1

Move $b$ .

$- 6 a^{3} + 4 a^{2} b + 3 b a - 1 \cdot 2 (b \cdot b)$

Step 2.1.9.2

Multiply $b$ by $b$ .

$- 6 a^{3} + 4 a^{2} b + 3 b a - 1 \cdot 2 b^{2}$

Step 2.1.10

Multiply $- 1$ by $2$ .

$- 6 a^{3} + 4 a^{2} b + 3 b a - 2 b^{2}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Move $b$ .

$- 6 a^{3} + 4 a^{2} b + 3 a b - 2 b^{2}$

Step 2.2.2

Move $3 a b$ .

$- 6 a^{3} + 4 a^{2} b - 2 b^{2} + 3 a b$

Step 2.2.3

Reorder $- 6 a^{3}$ and $4 a^{2} b$ .

$4 a^{2} b - 6 a^{3} - 2 b^{2} + 3 a b$