Algebra Examples

$6 a (2 a - b) + 2 a (- 4 a + 5 b)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$6 a (2 a) + 6 a (- b) + 2 a (- 4 a + 5 b)$

Step 1.2

Rewrite using the commutative property of multiplication.

$6 \cdot 2 a \cdot a + 6 a (- b) + 2 a (- 4 a + 5 b)$

Step 1.3

Rewrite using the commutative property of multiplication.

$6 \cdot 2 a \cdot a + 6 \cdot - 1 a b + 2 a (- 4 a + 5 b)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $a$ .

$6 \cdot 2 (a \cdot a) + 6 \cdot - 1 a b + 2 a (- 4 a + 5 b)$

Step 1.4.1.2

Multiply $a$ by $a$ .

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

Step 1.4.2

Multiply $6$ by $2$ .

$12 a^{2} + 6 \cdot - 1 a b + 2 a (- 4 a + 5 b)$

Step 1.4.3

Multiply $6$ by $- 1$ .

$12 a^{2} - 6 a b + 2 a (- 4 a + 5 b)$

Step 1.5

Apply the distributive property.

$12 a^{2} - 6 a b + 2 a (- 4 a) + 2 a (5 b)$

Step 1.6

Rewrite using the commutative property of multiplication.

$12 a^{2} - 6 a b + 2 \cdot - 4 a \cdot a + 2 a (5 b)$

Step 1.7

Rewrite using the commutative property of multiplication.

$12 a^{2} - 6 a b + 2 \cdot - 4 a \cdot a + 2 \cdot 5 a b$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $a$ .

$12 a^{2} - 6 a b + 2 \cdot - 4 (a \cdot a) + 2 \cdot 5 a b$

Step 1.8.1.2

Multiply $a$ by $a$ .

$12 a^{2} - 6 a b + 2 \cdot - 4 a^{2} + 2 \cdot 5 a b$

Step 1.8.2

Multiply $2$ by $- 4$ .

$12 a^{2} - 6 a b - 8 a^{2} + 2 \cdot 5 a b$

Step 1.8.3

Multiply $2$ by $5$ .

$12 a^{2} - 6 a b - 8 a^{2} + 10 a b$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 a^{2}$ from $12 a^{2}$ .

$4 a^{2} - 6 a b + 10 a b$

Step 2.2

Add $- 6 a b$ and $10 a b$ .

$4 a^{2} + 4 a b$