Question Simplify the product $(3x-4)(6x-2)$ using FOIL method. (1 point)

Studdy Solution

STEP 1

Assumptions
1. We will use the FOIL method to expand the product of two binomials.
2. FOIL stands for First, Outer, Inner, Last, which refers to the terms in each binomial that are multiplied together.
3. The given expression is $(3x - 4)(6x - 2)$ .

STEP 2

First, we will multiply the First terms in each binomial.
$First = 3x \times 6x$

STEP 3

Calculate the product of the First terms.
$First = 3x \times 6x = 18x^2$

STEP 4

Next, we will multiply the Outer terms in each binomial.
$Outer = 3x \times (-2)$

STEP 5

Calculate the product of the Outer terms.
$Outer = 3x \times (-2) = -6x$

STEP 6

Now, we will multiply the Inner terms in each binomial.
$Inner = (-4) \times 6x$

STEP 7

Calculate the product of the Inner terms.
$Inner = (-4) \times 6x = -24x$

STEP 8

Lastly, we will multiply the Last terms in each binomial.
$Last = (-4) \times (-2)$

STEP 9

Calculate the product of the Last terms.
$Last = (-4) \times (-2) = 8$

STEP 10

Now we will add all the products together to simplify the expression.
$Simplified\, expression = First + Outer + Inner + Last$

STEP 11

Substitute the calculated products into the simplified expression.
$Simplified\, expression = 18x^2 - 6x - 24x + 8$

STEP 12

Combine like terms.
$Simplified\, expression = 18x^2 - (6x + 24x) + 8$

STEP 13

Calculate the sum of the like terms.
$Simplified\, expression = 18x^2 - 30x + 8$
The simplified product using FOIL is $18x^2 - 30x + 8$ .

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