SOLUTION: Which of the following represents the product of 3 less than twice x and 2 more than the quanity 3 times x? a. -6x^2+25x+6 b. 6x^2+5x+6 c. 6x^2-5x+6 d. 6x^2-5x-6 e. 6x^2-13x-6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Which of the following represents the product of 3 less than twice x and 2 more than the quanity 3 times x? a. -6x^2+25x+6 b. 6x^2+5x+6 c. 6x^2-5x+6 d. 6x^2-5x-6 e. 6x^2-13x-6      Log On


   

Question 148487: Which of the following represents the product of 3 less than twice x and 2 more than the quanity 3 times x?
a. -6x^2+25x+6
b. 6x^2+5x+6
c. 6x^2-5x+6
d. 6x^2-5x-6
e. 6x^2-13x-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The expression "the product of 3 less than twice x and 2 more than the quanity 3 times x" translates to %282x-3%29%283x%2B2%29


So we need to expand %282x-3%29%283x%2B2%29



%282x-3%29%283x%2B2%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%282x%29-3%29%28highlight%283x%29%2B2%29 Multiply the First terms:%282%2Ax%29%2A%283%2Ax%29=6%2Ax%5E2.


%28highlight%282x%29-3%29%283x%2Bhighlight%282%29%29 Multiply the Outer terms:%282%2Ax%29%2A%282%29=4%2Ax.


%282x%2Bhighlight%28-3%29%29%28highlight%283x%29%2B2%29 Multiply the Inner terms:%28-3%29%2A%283%2Ax%29=-9%2Ax.


%282x%2Bhighlight%28-3%29%29%283x%2Bhighlight%282%29%29 Multiply the Last terms:%28-3%29%2A%282%29=-6.


6%2Ax%5E2%2B4%2Ax-9%2Ax-6 Now collect every term to make a single expression.


6%2Ax%5E2-5%2Ax-6 Now combine like terms.


So %282x-3%29%283x%2B2%29 FOILS to 6%2Ax%5E2-5%2Ax-6.


In other words, %282x-3%29%283x%2B2%29=6%2Ax%5E2-5%2Ax-6.


So this means that the answer is choice d)