Simplify ((t^2+3t-8)-(t^2-2t+6))(t-4)

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

Step 1

Simplify terms.

Simplify each term.

Apply the distributive property.

$(t^{2} + 3 t - 8 - t^{2} - (- 2 t) - 1 \cdot 6) (t - 4)$

Simplify.

Multiply $- 2$ by $- 1$ .

$(t^{2} + 3 t - 8 - t^{2} + 2 t - 1 \cdot 6) (t - 4)$

Multiply $- 1$ by $6$ .

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

Simplify by adding terms.

Combine the opposite terms in $t^{2} + 3 t - 8 - t^{2} + 2 t - 6$ .

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

$(3 t - 8 + 0 + 2 t - 6) (t - 4)$

Add $3 t - 8$ and $0$ .

$(3 t - 8 + 2 t - 6) (t - 4)$

Add $3 t$ and $2 t$ .

$(5 t - 8 - 6) (t - 4)$

Subtract $6$ from $- 8$ .

$(5 t - 14) (t - 4)$

Step 2

Expand $(5 t - 14) (t - 4)$ using the FOIL Method.

Apply the distributive property.

$5 t (t - 4) - 14 (t - 4)$

Apply the distributive property.

$5 t \cdot t + 5 t \cdot - 4 - 14 (t - 4)$

Apply the distributive property.

$5 t \cdot t + 5 t \cdot - 4 - 14 t - 14 \cdot - 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$5 (t \cdot t) + 5 t \cdot - 4 - 14 t - 14 \cdot - 4$

Multiply $t$ by $t$ .

$5 t^{2} + 5 t \cdot - 4 - 14 t - 14 \cdot - 4$

Multiply $- 4$ by $5$ .

$5 t^{2} - 20 t - 14 t - 14 \cdot - 4$

Multiply $- 14$ by $- 4$ .

$5 t^{2} - 20 t - 14 t + 56$

Subtract $14 t$ from $- 20 t$ .

$5 t^{2} - 34 t + 56$