Simplify (2a^2-b)(-3a+2b)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $- 3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $- 3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $- 1$ by $2$ .

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

Simplify the expression.

Move $b$ .

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

Move $3 a b$ .

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

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

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

Simplify (2a^2-b)(-3a+2b)

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