Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $3$ by $5$ .

$15 t + 5 \cdot - 4 - (t^{2} + 2) - 2 t (t - 3)$

Step 1.3

Multiply $5$ by $- 4$ .

$15 t - 20 - (t^{2} + 2) - 2 t (t - 3)$

Step 1.4

Apply the distributive property.

$15 t - 20 - t^{2} - 1 \cdot 2 - 2 t (t - 3)$

Step 1.5

Multiply $- 1$ by $2$ .

$15 t - 20 - t^{2} - 2 - 2 t (t - 3)$

Step 1.6

Apply the distributive property.

$15 t - 20 - t^{2} - 2 - 2 t \cdot t - 2 t \cdot - 3$

Step 1.7

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

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Step 1.7.1

Move $t$ .

$15 t - 20 - t^{2} - 2 - 2 (t \cdot t) - 2 t \cdot - 3$

Step 1.7.2

Multiply $t$ by $t$ .

$15 t - 20 - t^{2} - 2 - 2 t^{2} - 2 t \cdot - 3$

Step 1.8

Multiply $- 3$ by $- 2$ .

$15 t - 20 - t^{2} - 2 - 2 t^{2} + 6 t$

Step 2

Simplify by adding terms.

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Step 2.1

Add $15 t$ and $6 t$ .

$21 t - 20 - t^{2} - 2 - 2 t^{2}$

Step 2.2

Subtract $2$ from $- 20$ .

$21 t - t^{2} - 22 - 2 t^{2}$

Step 2.3

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

$21 t - 3 t^{2} - 22$

Step 2.4

Reorder $21 t$ and $- 3 t^{2}$ .

$- 3 t^{2} + 21 t - 22$