Simplify (7t^2+6t-1)-(3t-5t^2+4-t^3)

$(7 t^{2} + 6 t - 1) - (3 t - 5 t^{2} + 4 - t^{3})$

Step 1

Simplify each term.

Apply the distributive property.

$7 t^{2} + 6 t - 1 - (3 t) - (- 5 t^{2}) - 1 \cdot 4 - - t^{3}$

Simplify.

Multiply $3$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t - (- 5 t^{2}) - 1 \cdot 4 - - t^{3}$

Multiply $- 5$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 1 \cdot 4 - - t^{3}$

Multiply $- 1$ by $4$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 - - t^{3}$

Multiply $- - t^{3}$ .

Multiply $- 1$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 + 1 t^{3}$

Multiply $t^{3}$ by $1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 + t^{3}$

Step 2

Simplify by adding terms.

Add $7 t^{2}$ and $5 t^{2}$ .

$12 t^{2} + 6 t - 1 - 3 t - 4 + t^{3}$

Subtract $3 t$ from $6 t$ .

$12 t^{2} + 3 t - 1 - 4 + t^{3}$

Simplify the expression.

Subtract $4$ from $- 1$ .

$12 t^{2} + 3 t - 5 + t^{3}$

Move $- 5$ .

$12 t^{2} + 3 t + t^{3} - 5$

Move $3 t$ .

$12 t^{2} + t^{3} + 3 t - 5$

Reorder $12 t^{2}$ and $t^{3}$ .

$t^{3} + 12 t^{2} + 3 t - 5$