Algebra Examples

$(2 x^{2} + 1) - (x^{2} - 2 x + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x^{2} + 1 - x^{2} - (- 2 x) - 1 \cdot 1$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 2$ by $- 1$ .

$2 x^{2} + 1 - x^{2} + 2 x - 1 \cdot 1$

Step 1.2.2

Multiply $- 1$ by $1$ .

$2 x^{2} + 1 - x^{2} + 2 x - 1$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $2 x^{2} + 1 - x^{2} + 2 x - 1$ .

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Step 2.1.1

Subtract $1$ from $1$ .

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

Step 2.1.2

Add $2 x^{2} - x^{2} + 2 x$ and $0$ .

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

Step 2.2

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

$x^{2} + 2 x$