Basic Math Examples

$a^{2} + b^{2} + c^{2} + 2 a c + 2 a c + 2 b c + (- 0^{2} + 2 b^{2} - c^{2} + 4 a b - 4 a c + 4 b c)$

Step 1

Simplify by adding terms.

Tap for more steps...

Step 1.1

Remove parentheses.

$a^{2} + b^{2} + c^{2} + 2 a c + 2 a c + 2 b c - 0^{2} + 2 b^{2} - c^{2} + 4 a b - 4 a c + 4 b c$

Step 1.2

Combine the opposite terms in $a^{2} + b^{2} + c^{2} + 2 a c + 2 a c + 2 b c - 0^{2} + 2 b^{2} - c^{2} + 4 a b - 4 a c + 4 b c$ .

Tap for more steps...

Step 1.2.1

Subtract $c^{2}$ from $c^{2}$ .

$a^{2} + b^{2} + 2 a c + 2 a c + 2 b c - 0^{2} + 2 b^{2} + 0 + 4 a b - 4 a c + 4 b c$

Step 1.2.2

Add $a^{2} + b^{2} + 2 a c + 2 a c + 2 b c - 0^{2} + 2 b^{2}$ and $0$ .

$a^{2} + b^{2} + 2 a c + 2 a c + 2 b c - 0^{2} + 2 b^{2} + 4 a b - 4 a c + 4 b c$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Raising $0$ to any positive power yields $0$ .

$a^{2} + b^{2} + 2 a c + 2 a c + 2 b c - 0 + 2 b^{2} + 4 a b - 4 a c + 4 b c$

Step 2.2

Multiply $- 1$ by $0$ .

$a^{2} + b^{2} + 2 a c + 2 a c + 2 b c + 0 + 2 b^{2} + 4 a b - 4 a c + 4 b c$

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Add $a^{2} + b^{2} + 2 a c + 2 a c + 2 b c$ and $0$ .

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

Step 3.2

Add $b^{2}$ and $2 b^{2}$ .

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

Step 3.3

Add $2 a c$ and $2 a c$ .

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

Step 3.4

Combine the opposite terms in $a^{2} + 3 b^{2} + 4 a c + 2 b c + 4 a b - 4 a c + 4 b c$ .

Tap for more steps...

Step 3.4.1

Subtract $4 a c$ from $4 a c$ .

$a^{2} + 3 b^{2} + 2 b c + 4 a b + 0 + 4 b c$

Step 3.4.2

Add $a^{2} + 3 b^{2} + 2 b c + 4 a b$ and $0$ .

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

Step 3.5

Add $2 b c$ and $4 b c$ .

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