Simplify (7r^3+6+7r^2-4r^4)-(-7r^4+8r^2-8r^3-8)

$(7 r^{3} + 6 + 7 r^{2} - 4 r^{4}) - (- 7 r^{4} + 8 r^{2} - 8 r^{3} - 8)$

Step 1

Simplify each term.

Apply the distributive property.

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} - (- 7 r^{4}) - (8 r^{2}) - (- 8 r^{3}) - - 8$

Simplify.

Multiply $- 7$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - (8 r^{2}) - (- 8 r^{3}) - - 8$

Multiply $8$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} - (- 8 r^{3}) - - 8$

Multiply $- 8$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8 r^{3} - - 8$

Multiply $- 1$ by $- 8$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8 r^{3} + 8$

Step 2

Simplify by adding terms.

Add $7 r^{3}$ and $8 r^{3}$ .

$15 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8$

Add $6$ and $8$ .

$15 r^{3} + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 14$

Subtract $8 r^{2}$ from $7 r^{2}$ .

$15 r^{3} - 4 r^{4} + 7 r^{4} - r^{2} + 14$

Add $- 4 r^{4}$ and $7 r^{4}$ .

$15 r^{3} + 3 r^{4} - r^{2} + 14$

Reorder $15 r^{3}$ and $3 r^{4}$ .

$3 r^{4} + 15 r^{3} - r^{2} + 14$