Simplify (3+x-x^2)-(-4x^2+2x+1)

$(3 + x - x^{2}) - (- 4 x^{2} + 2 x + 1)$

Step 1

Simplify each term.

Apply the distributive property.

$3 + x - x^{2} - (- 4 x^{2}) - (2 x) - 1 \cdot 1$

Simplify.

Multiply $- 4$ by $- 1$ .

$3 + x - x^{2} + 4 x^{2} - (2 x) - 1 \cdot 1$

Multiply $2$ by $- 1$ .

$3 + x - x^{2} + 4 x^{2} - 2 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$3 + x - x^{2} + 4 x^{2} - 2 x - 1$

$3 + x - x^{2} + 4 x^{2} - 2 x - 1$

$3 + x - x^{2} + 4 x^{2} - 2 x - 1$

Step 2

Simplify by adding terms.

Subtract $1$ from $3$ .

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

Subtract $2 x$ from $x$ .

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

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

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

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

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