c(t)=2(t-4)(t+1)(t-6)
Mathematics · College · Tue Nov 03 2020
Answered on
Given the function:
c(t)=2(t-4)(t+1)(t-6)
Solution:
In order to simplify it we will use the foil method on each expression, then multiply the final answer by 2. To use the FOIL method in solving for the given numerical expression. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (t)(t)
=t^2
First term of the first equation multiplied to the first term of the third equation.
=(t)(1)
= t
First term of the first equation multiplied to the last term of the second equation.
=(-4)(t)
=-4t
Last term of the first equation multiplied to the first term of the second equation.
=(-4)(-1)
= 4
Last term of the first equation multiplied to the last term of the second equation.
___________________________________________________________________________________________________________________
= (t)(t)
=t^2
First term of the first equation multiplied to the first term of the third equation.
=(t)(-6)
= -6t
Last term of the first equation multiplied to the last term of the third equation.
=(-4)(t)
=-4t
Last term of the first equation multiplied to the first term of the third equation.
=(-4)(-6)
= 24
Last term of the first equation multiplied to the last term of the third equation.
___________________________________________________________________________________________________________________
= (t)(t)
=t^2
First term of the second equation multiplied to the first term of the third equation.
=(t)(-6)
= -6t
Last term of the second equation multiplied to the last term of the third equation.
=(1)(t)
=t
Last term of the second equation multiplied to the first term of the third equation.
=(1)(-6)
= -6
Last term of the second equation multiplied to the last term of the third equation.
Combined answer:
=t^2 + t - 4t + 4 +t^2 -6t -4t + 24 +t^2 -6t + t -6
= 3t^2 - 18t +22
Multiply the answer by 2.
= 2(3t^2 - 18t +22)
= 6t^2 - 36t + 44