Perform the indicated operations and simplify. $3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )$
A) $- 6 t ^ { 2 } - 19 t + 26$
B) $- 6 t ^ { 2 } + 19 t - 18$
C) $- 6 t ^ { 2 } + 14 t - 18$
D) $- 9 t ^ { 2 } + 14 t - 26$
E) $- 6 t ^ { 2 } + 19 t + 18$

Question

Quizplus · Accepted Answer

We start by expanding all the terms:

$3(3t-5) = 9t - 15$
$-(t^2+3) = -t^2 - 3$
$-5t(t-2) = -5t^2 + 10t$

Substituting these values back into the equation:

$3(3t-5) - (t^2+3) - 5t(t-2) = (9t-15) - (t^2+3) - (-5t^2+10t)$
$= 9t - 15 - t^2 - 3 + 5t^2 - 10t$
$= -6t^2 + 19t - 18$

Thus, the answer is B.

Perform the Indicated Operations and Simplify 3(3t−5)−(t2+3)−5t(t−2)3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )3(3t−5)−(t2+3)−5t(t−2)

Perform the Indicated Operations and Simplify $3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )$