Basic Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

Step 1.2.2

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

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

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

Step 1.2.3

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

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

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

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

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

Step 1.3

Remove parentheses.

3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} + 2 b c

$3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} + 2 b c$

3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} + 2 b c

$3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} + 2 b c$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

2 a b

$2 a b$ from

3 a b

$3 a b$ .

3 a^{2} + 1 a b + 3 a c + 2 b^{2} + 2 b c

$3 a^{2} + 1 a b + 3 a c + 2 b^{2} + 2 b c$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply

a

$a$ by

1

$1$ .

3 a^{2} + a b + 3 a c + 2 b^{2} + 2 b c

$3 a^{2} + a b + 3 a c + 2 b^{2} + 2 b c$

Step 2.2.2

Move

2 b^{2}

$2 b^{2}$ .

3 a^{2} + a b + 3 a c + 2 b c + 2 b^{2}

$3 a^{2} + a b + 3 a c + 2 b c + 2 b^{2}$

Step 2.2.3

Move

a b

$a b$ .

3 a^{2} + 3 a c + 2 b c + a b + 2 b^{2}

$3 a^{2} + 3 a c + 2 b c + a b + 2 b^{2}$

Step 2.2.4

Move

3 a^{2}

$3 a^{2}$ .

3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}

$3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}$

3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}

$3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}$

3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}

$3 a c + 2 b c + 3 a^{2} + a b + 2 b^{2}$