Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply

$3$ by

$- 1$ .

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

Step 1.2.2

Multiply

$- 2$ by

$- 1$ .

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

Step 1.2.3

Multiply

$2$ by

$- 1$ .

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

Step 1.2.4

Multiply

$- 3$ by

$- 1$ .

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

Step 1.3

Remove parentheses.

$- 4 a c + 4 b c + 4 c^{2} - 3 a c + 2 b c - 2 b^{2} - a b + 3 a^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

$3 a c$ from

$- 4 a c$ .

$4 b c + 4 c^{2} - 7 a c + 2 b c - 2 b^{2} - a b + 3 a^{2}$

Step 2.2

Add

$4 b c$ and

$2 b c$ .

$4 c^{2} - 7 a c + 6 b c - 2 b^{2} - a b + 3 a^{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move

$4 c^{2}$ .

$- 7 a c + 6 b c - 2 b^{2} - a b + 3 a^{2} + 4 c^{2}$

Step 2.3.2

Move

$6 b c$ .

$- 7 a c - 2 b^{2} - a b + 3 a^{2} + 6 b c + 4 c^{2}$

Step 2.3.3

Move

$- 2 b^{2}$ .

$- 7 a c - a b + 3 a^{2} - 2 b^{2} + 6 b c + 4 c^{2}$

Step 2.3.4

Move

$- 7 a c$ .

$- a b + 3 a^{2} - 7 a c - 2 b^{2} + 6 b c + 4 c^{2}$

Step 2.3.5

Reorder

$- a b$ and

$3 a^{2}$ .

$3 a^{2} - a b - 7 a c - 2 b^{2} + 6 b c + 4 c^{2}$