Simplify (2x-3)+(2x-5x^2+13)-(x^2-1)

$(2 x - 3) + (2 x - 5 x^{2} + 13) - (x^{2} - 1)$

Step 1

Remove parentheses.

$2 x - 3 + 2 x - 5 x^{2} + 13 - (x^{2} - 1)$

Step 2

Simplify each term.

Apply the distributive property.

$2 x - 3 + 2 x - 5 x^{2} + 13 - x^{2} - - 1$

Multiply $- 1$ by $- 1$ .

$2 x - 3 + 2 x - 5 x^{2} + 13 - x^{2} + 1$

$2 x - 3 + 2 x - 5 x^{2} + 13 - x^{2} + 1$

Step 3

Simplify by adding terms.

Add $2 x$ and $2 x$ .

$4 x - 3 - 5 x^{2} + 13 - x^{2} + 1$

Add $- 3$ and $13$ .

$4 x - 5 x^{2} + 10 - x^{2} + 1$

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

$4 x - 6 x^{2} + 10 + 1$

Simplify the expression.

Add $10$ and $1$ .

$4 x - 6 x^{2} + 11$

Reorder $4 x$ and $- 6 x^{2}$ .

$- 6 x^{2} + 4 x + 11$

$- 6 x^{2} + 4 x + 11$

$- 6 x^{2} + 4 x + 11$

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