Simplify (t^4-t^2+t)-(12-9t^2-7t)

$(t^{4} - t^{2} + t) - (12 - 9 t^{2} - 7 t)$

Simplify each term.

Apply the distributive property.

$t^{4} - t^{2} + t - 1 \cdot 12 - (- 9 t^{2}) - (- 7 t)$

Simplify.

Multiply $- 1$ by $12$ .

$t^{4} - t^{2} + t - 12 - (- 9 t^{2}) - (- 7 t)$

Multiply $- 9$ by $- 1$ .

$t^{4} - t^{2} + t - 12 + 9 t^{2} - (- 7 t)$

Multiply $- 7$ by $- 1$ .

$t^{4} - t^{2} + t - 12 + 9 t^{2} + 7 t$

Simplify by adding terms.

Add $- t^{2}$ and $9 t^{2}$ .

$t^{4} + 8 t^{2} + t - 12 + 7 t$

Add $t$ and $7 t$ .

$t^{4} + 8 t^{2} + 8 t - 12$