Algebra Examples

Subtract $(- a^{2} - 5 a b + 3 b^{2})$ from $(3 a^{2} - 2 a b + 3 b^{2})$

Step 1

Write the problem as a mathematical expression.

$(3 a^{2} - 2 a b + 3 b^{2}) - (- a^{2} - 5 a b + 3 b^{2})$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 a^{2} - 2 a b + 3 b^{2} - - a^{2} - (- 5 a b) - (3 b^{2})$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $- - a^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply $- 1$ by $- 1$ .

$3 a^{2} - 2 a b + 3 b^{2} + 1 a^{2} - (- 5 a b) - (3 b^{2})$

Step 2.2.1.2

Multiply $a^{2}$ by $1$ .

$3 a^{2} - 2 a b + 3 b^{2} + a^{2} - (- 5 a b) - (3 b^{2})$

Step 2.2.2

Multiply $- 5$ by $- 1$ .

$3 a^{2} - 2 a b + 3 b^{2} + a^{2} + 5 (a b) - (3 b^{2})$

Step 2.2.3

Multiply $3$ by $- 1$ .

$3 a^{2} - 2 a b + 3 b^{2} + a^{2} + 5 (a b) - 3 b^{2}$

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

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $3 a^{2} - 2 a b + 3 b^{2} + a^{2} + 5 a b - 3 b^{2}$ .

Tap for more steps...

Step 3.1.1

Subtract $3 b^{2}$ from $3 b^{2}$ .

$3 a^{2} - 2 a b + a^{2} + 5 a b + 0$

Step 3.1.2

Add $3 a^{2} - 2 a b + a^{2} + 5 a b$ and $0$ .

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

Step 3.2

Add $3 a^{2}$ and $a^{2}$ .

$4 a^{2} - 2 a b + 5 a b$

Step 3.3

Add $- 2 a b$ and $5 a b$ .

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