Simplify (2w^2+w+4)-2w^2+4w-8(-6w^2-5w+6)

$(2 w^{2} + w + 4) - 2 w^{2} + 4 w - 8 (- 6 w^{2} - 5 w + 6)$

Step 1

Combine the opposite terms in $(2 w^{2} + w + 4) - 2 w^{2} + 4 w - 8 (- 6 w^{2} - 5 w + 6)$ .

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

$w + 4 + 0 + 4 w - 8 (- 6 w^{2} - 5 w + 6)$

Add $w + 4$ and $0$ .

$w + 4 + 4 w - 8 (- 6 w^{2} - 5 w + 6)$

Step 2

Simplify each term.

Apply the distributive property.

$w + 4 + 4 w - 8 (- 6 w^{2}) - 8 (- 5 w) - 8 \cdot 6$

Simplify.

Multiply $- 6$ by $- 8$ .

$w + 4 + 4 w + 48 w^{2} - 8 (- 5 w) - 8 \cdot 6$

Multiply $- 5$ by $- 8$ .

$w + 4 + 4 w + 48 w^{2} + 40 w - 8 \cdot 6$

Multiply $- 8$ by $6$ .

$w + 4 + 4 w + 48 w^{2} + 40 w - 48$

Step 3

Simplify by adding terms.

Add $w$ and $4 w$ .

$5 w + 4 + 48 w^{2} + 40 w - 48$

Add $5 w$ and $40 w$ .

$45 w + 4 + 48 w^{2} - 48$

Simplify the expression.

Subtract $48$ from $4$ .

$45 w + 48 w^{2} - 44$

Reorder $45 w$ and $48 w^{2}$ .

$48 w^{2} + 45 w - 44$