Basic Math Examples

$2 a (a - 6 b) - 3 b (a - 6 b) - 2 (a - 6 b)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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Step 1.2.1

Move $a$ .

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

Step 1.2.2

Multiply $a$ by $a$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Multiply $2$ by $- 6$ .

$2 a^{2} - 12 a b - 3 b (a - 6 b) - 2 (a - 6 b)$

Step 1.5

Apply the distributive property.

$2 a^{2} - 12 a b - 3 b a - 3 b (- 6 b) - 2 (a - 6 b)$

Step 1.6

Rewrite using the commutative property of multiplication.

$2 a^{2} - 12 a b - 3 b a - 3 \cdot - 6 b \cdot b - 2 (a - 6 b)$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $b$ .

$2 a^{2} - 12 a b - 3 b a - 3 \cdot - 6 (b \cdot b) - 2 (a - 6 b)$

Step 1.7.1.2

Multiply $b$ by $b$ .

$2 a^{2} - 12 a b - 3 b a - 3 \cdot - 6 b^{2} - 2 (a - 6 b)$

Step 1.7.2

Multiply $- 3$ by $- 6$ .

$2 a^{2} - 12 a b - 3 b a + 18 b^{2} - 2 (a - 6 b)$

Step 1.8

Apply the distributive property.

$2 a^{2} - 12 a b - 3 b a + 18 b^{2} - 2 a - 2 (- 6 b)$

Step 1.9

Multiply $- 6$ by $- 2$ .

$2 a^{2} - 12 a b - 3 b a + 18 b^{2} - 2 a + 12 b$

Step 2

Subtract $3 b a$ from $- 12 a b$ .

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Step 2.1

Move $b$ .

$2 a^{2} - 12 a b - 3 a b + 18 b^{2} - 2 a + 12 b$

Step 2.2

Subtract $3 a b$ from $- 12 a b$ .

$2 a^{2} - 15 a b + 18 b^{2} - 2 a + 12 b$