Simplify (x^2+2x-5)-(3x^2-4x+7)

$(x^{2} + 2 x - 5) - (3 x^{2} - 4 x + 7)$

Step 1

Simplify each term.

Apply the distributive property.

$x^{2} + 2 x - 5 - (3 x^{2}) - (- 4 x) - 1 \cdot 7$

Simplify.

Multiply $3$ by $- 1$ .

$x^{2} + 2 x - 5 - 3 x^{2} - (- 4 x) - 1 \cdot 7$

Multiply $- 4$ by $- 1$ .

$x^{2} + 2 x - 5 - 3 x^{2} + 4 x - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$x^{2} + 2 x - 5 - 3 x^{2} + 4 x - 7$

Step 2

Simplify by adding terms.

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

$- 2 x^{2} + 2 x - 5 + 4 x - 7$

Add $2 x$ and $4 x$ .

$- 2 x^{2} + 6 x - 5 - 7$

Subtract $7$ from $- 5$ .

$- 2 x^{2} + 6 x - 12$