Simplify (2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)

$(2 x^{2} + x + 1) - (x^{2} - x + 7) - (4 x^{2} + 2 x + 8)$

Step 1

Simplify each term.

Apply the distributive property.

$2 x^{2} + x + 1 - x^{2} - - x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$2 x^{2} + x + 1 - x^{2} + 1 x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Multiply $x$ by $1$ .

$2 x^{2} + x + 1 - x^{2} + x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Multiply $- 1$ by $7$ .

$2 x^{2} + x + 1 - x^{2} + x - 7 - (4 x^{2} + 2 x + 8)$

Apply the distributive property.

$2 x^{2} + x + 1 - x^{2} + x - 7 - (4 x^{2}) - (2 x) - 1 \cdot 8$

Simplify.

Multiply $4$ by $- 1$ .

$2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - (2 x) - 1 \cdot 8$

Multiply $2$ by $- 1$ .

$2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - 2 x - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - 2 x - 8$

Step 2

Simplify by adding terms.

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

$x^{2} + x + 1 + x - 7 - 4 x^{2} - 2 x - 8$

Subtract $4 x^{2}$ from $x^{2}$ .

$- 3 x^{2} + x + 1 + x - 7 - 2 x - 8$

Add $x$ and $x$ .

$- 3 x^{2} + 2 x + 1 - 7 - 2 x - 8$

Combine the opposite terms in $- 3 x^{2} + 2 x + 1 - 7 - 2 x - 8$ .

Subtract $2 x$ from $2 x$ .

$- 3 x^{2} + 0 + 1 - 7 - 8$

Add $- 3 x^{2}$ and $0$ .

$- 3 x^{2} + 1 - 7 - 8$

Simplify by subtracting numbers.

Subtract $7$ from $1$ .

$- 3 x^{2} - 6 - 8$

Subtract $8$ from $- 6$ .

$- 3 x^{2} - 14$