Write in Standard Form (2x^2+1)-(x^2-2x+1)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $- 2$ by $- 1$ .

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

Multiply $- 1$ by $1$ .

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

Step 3

Simplify by adding terms.

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

Subtract $1$ from $1$ .

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

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

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

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

$x^{2} + 2 x$