Chemistry Examples

$(- 8 a) (4 a + 3 b - 2 c)$

Step 1

Apply the distributive property.

$- 8 a (4 a) - 8 a (3 b) - 8 a (- 2 c)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 8 \cdot 4 a \cdot a - 8 a (3 b) - 8 a (- 2 c)$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 8 \cdot 4 a \cdot a - 8 \cdot 3 a b - 8 a (- 2 c)$

Step 2.3

Rewrite using the commutative property of multiplication.

$- 8 \cdot 4 a \cdot a - 8 \cdot 3 a b - 8 \cdot - 2 a c$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $a$ .

$- 8 \cdot 4 (a \cdot a) - 8 \cdot 3 a b - 8 \cdot - 2 a c$

Step 3.1.2

Multiply $a$ by $a$ .

$- 8 \cdot 4 a^{2} - 8 \cdot 3 a b - 8 \cdot - 2 a c$

Step 3.2

Multiply $- 8$ by $4$ .

$- 32 a^{2} - 8 \cdot 3 a b - 8 \cdot - 2 a c$

Step 3.3

Multiply $- 8$ by $3$ .

$- 32 a^{2} - 24 a b - 8 \cdot - 2 a c$

Step 3.4

Multiply $- 8$ by $- 2$ .

$- 32 a^{2} - 24 a b + 16 a c$