Algebra Examples

$(3 x^{2} + 2 y^{2} - 3 x) + (2 x^{2} + y^{2} - 2 x) - (x^{2} + 3 y^{2} + x)$

Step 1

Remove parentheses.

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - (x^{2} + 3 y^{2} + x)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - x^{2} - (3 y^{2}) - x$

Step 2.2

Multiply $3$ by $- 1$ .

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - x^{2} - 3 y^{2} - x$

Step 3

Simplify by adding terms.

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Step 3.1

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

$5 x^{2} + 2 y^{2} - 3 x + y^{2} - 2 x - x^{2} - 3 y^{2} - x$

Step 3.2

Subtract $x^{2}$ from $5 x^{2}$ .

$4 x^{2} + 2 y^{2} - 3 x + y^{2} - 2 x - 3 y^{2} - x$

Step 3.3

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

$4 x^{2} + 3 y^{2} - 3 x - 2 x - 3 y^{2} - x$

Step 3.4

Combine the opposite terms in $4 x^{2} + 3 y^{2} - 3 x - 2 x - 3 y^{2} - x$ .

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Step 3.4.1

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

$4 x^{2} - 3 x - 2 x + 0 - x$

Step 3.4.2

Add $4 x^{2} - 3 x - 2 x$ and $0$ .

$4 x^{2} - 3 x - 2 x - x$

Step 3.5

Subtract $2 x$ from $- 3 x$ .

$4 x^{2} - 5 x - x$

Step 3.6

Subtract $x$ from $- 5 x$ .

$4 x^{2} - 6 x$