Choose an option and show work

Question

The expression (4z + 3)(z - 2) is equivalent to:

 

A. 4z^2 - 5

B. 4z^2 - 6

C. 4z^2 - 3z - 5

D. 4z^2 - 5z - 6

E. 4z^2 + 5z - 6

Answer 1

Use F-O-I-L:  

                     First       Outside       Inside       Last

 (a+b)(c+d) = ac   +      ad        +     bc     +    bd

 

                     First       Outside       Inside       Last

(4z+3)(z-2)=    4z²   -      8z       +     3z      -    6

                      4z²             -   5z                 -   6        (collect like terms)

Answer 2

To multiply two expressions together, you must multiply each term in the first expression by each term in the second expression.

 

Start with 4z:  (4z)(z) + (4z)(-2) = 4z² - 8z

Now multiply "+3" times each term in the second expression:  (3)(z) + (3)(-2) = 3z - 6

 

Now combine the two results and simplify similar terms:

4z² - 8z + 3z - 6

 

4z² -5z -6

 

Choice "D" is the correct answer.