QuestionMultiply $(x-4)(2 x+3)$ using the FOIL method. Which option shows the FOIL products? A, B, C, or D?

Studdy Solution

STEP 1

Assumptions1. We are asked to multiply $(x-4)( x+3)$ using the FOIL method. . The FOIL method stands for First, Outer, Inner, Last. It is a method used for multiplying binomials.
3. The FOIL method involves four multiplications, each corresponding to a word in the acronym FOIL.

STEP 2

First, we multiply the first terms in each binomial. This corresponds to the '' in FOIL.
$First = x \times2x$

STEP 3

Calculate the product of the first terms.
$First = x \times2x =2x^2$

STEP 4

Next, we multiply the outer terms in the expression. This corresponds to the '' in FOIL.
$Outer = x \times3$

STEP 5

Calculate the product of the outer terms.
$Outer = x \times3 =3x$

STEP 6

Then, we multiply the inner terms in the expression. This corresponds to the '' in FOIL.
$Inner = -4 \times2x$

STEP 7

Calculate the product of the inner terms.
$Inner = -4 \times2x = -x$

STEP 8

Finally, we multiply the last terms in each binomial. This corresponds to the '' in FOIL.
$Last = -4 \times3$

STEP 9

Calculate the product of the last terms.
$Last = -4 \times3 = -12$

STEP 10

Now, we add the results of the four multiplications together to get the final result.
$Result = First + Outer + Inner + Last$

STEP 11

Plug in the values for First, Outer, Inner, and Last to calculate the result.
$Result =x^ +3x -8x -$

STEP 12

Combine like terms in the result.
$Result =2x^2 -5x -12$ So, the product of $(x-4)(2 x+)$ using the FOIL method is $2x^2 -5x -12$ . The correct answer choice is D $(x)(2 x)+(x)+(-4)(2 x)+(-4)()$ .

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