Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 a \cdot a + 3 a (- b) - 4 a (2 a + 3 b)$

Step 1.2

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

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Step 1.2.1

Move $a$ .

$3 (a \cdot a) + 3 a (- b) - 4 a (2 a + 3 b)$

Step 1.2.2

Multiply $a$ by $a$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Multiply $3$ by $- 1$ .

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Rewrite using the commutative property of multiplication.

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

Step 1.7

Rewrite using the commutative property of multiplication.

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

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 $a$ .

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

Step 1.8.1.2

Multiply $a$ by $a$ .

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

Step 1.8.2

Multiply $- 4$ by $2$ .

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

Step 1.8.3

Multiply $- 4$ by $3$ .

$3 a^{2} - 3 a b - 8 a^{2} - 12 a b$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 a^{2}$ from $3 a^{2}$ .

$- 5 a^{2} - 3 a b - 12 a b$

Step 2.2

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

$- 5 a^{2} - 15 a b$