What is 5(3t-4)-(t^2+2)-2t(t-3) ?

The solution to 5(3t-4)-(t^2+2)-2t(t-3) is -3t^2+21t-22

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simplify 5(3t-4)-(t^2+2)-2t(t-3)

simplify

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

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

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

- (t^{2} + 2) = - t^{2} - 2

= 5 (3 t - 4) - t^{2} - 2 - 2 t (t - 3)

Expand

5 (3 t - 4) : 15 t - 20

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

Expand

- 2 t (t - 3) : - 2 t^{2} + 6 t

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

Group like terms

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

Add similar elements:

- t^{2} - 2 t^{2} = - 3 t^{2}

= - 3 t^{2} + 15 t + 6 t - 20 - 2

Add similar elements:

15 t + 6 t = 21 t

= - 3 t^{2} + 21 t - 20 - 2

Subtract the numbers:

- 20 - 2 = - 22

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

(3 + 2)^{2}

csc^{3} (x) - csc^{2} (x) - csc (x) + 1

\frac{2 y}{y - 3} \cdot \frac{4 y - 12}{2 y + 6}

\frac{23}{8}

\frac{5 x}{x - 6} + \frac{1}{x - 6}

What is 5(3t-4)-(t^2+2)-2t(t-3) ?
The solution to 5(3t-4)-(t^2+2)-2t(t-3) is -3t^2+21t-22