Question Expand the product of two binomials using the FOIL method, then combine like terms. $(6x+1)(2x+1)$

Studdy Solution

STEP 1

Assumptions1. We are given two binomials $(6x+1)$ and $(x+1)$ . . We need to multiply these binomials using the FOIL method.
3. FOIL stands for First, Outer, Inner, Last, which is a method for multiplying binomials.

STEP 2

First, we multiply the first terms in each binomial.
$First =6x \\times2x$

STEP 3

Calculate the product of the first terms.
$First =6x \\times2x =12x^2$

STEP 4

Next, we multiply the outer terms in each binomial.
$Outer =6x \\times1$

STEP 5

Calculate the product of the outer terms.
$Outer =x \\times1 =x$

STEP 6

Then, we multiply the inner terms in each binomial.
$Inner =1 \\times2x$

STEP 7

Calculate the product of the inner terms.
$Inner =1 \\times2x =2x$

STEP 8

Finally, we multiply the last terms in each binomial.
$Last =1 \\times1$

STEP 9

Calculate the product of the last terms.
$Last = \\times =$

STEP 10

Now, we add all these products together.
$Product = First + Outer + Inner + Last$

STEP 11

Plug in the values for First, Outer, Inner, and Last to calculate the product.
$Product =x^ +6x +x +$

STEP 12

Combine like terms.
$Product =12x^2 + (6x +2x) +$

STEP 13

Calculate the sum of the like terms.
$Product =12x^2 +8x +$ The product of the binomials $(6x+)$ and $(2x+)$ is $12x^2 +8x +$ .

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