What is (3x+1)(4x+2)?

Question

Please solve (3x+1)(4x+2) and explain.

Answer 1

This is an expression, not an equation. So there's nothing to "solve". But it can be expanded, if that's what you're trying to do. Just use the distributive rule twice:

(3x+1)(4x+2) =
3x(4x+2) + 1*(4x+2) =
12x^2 + 6x + (4x+2) =
12x^2 + 10x + 2

Answer 2

To find the product of two polynomials, you take each term on the left and multiply it by every term on the right, and do this for all the terms on the left. In this example, you have:

3x*4x + 3x*2 + 1*4x + 1*2

Simplifying:

12x² + 6x + 4x + 2
12x² + 10x + 2

The reason this works is a simple application of the distributive property. Using this example again, we have:

(3x+1)(4x+2)

Distributing the (4x+2)

3x*(4x+2) + 1*(4x+2)

And now distributing the 3x and the 1:

3x*4x + 3x*2 + 1*4x + 1*2.

Sometimes, in the special case of the product of two binomials, the acronym FOIL (first, outer, inner, last) is used to help the student remember all the terms they are supposed to multiply. I dislike this acronym for two reasons: first, many students get the impression that the order matters from listening to the algorithm. It doesn't -- addition is commutative, so what matters is that all the terms are there, not which order they are listed in (sometimes when taking complicated products it can be helpful to know this). The second reason is that it offers no insight on how to multiply, say, (x²+9x-2)*(x²-9x-2). But the procedure is the same: multiply everything on the left by everything on the right. So we have:

x²*x² + x²*(-9x) + x²*(-2) + 9x*x² + 9x*(-9x) + 9x*(-2) + (-2)*x² + (-2)*(-9x) + (-2)*(-2).

Simplifying:

x⁴ - 9x³ - 2x² + 9x³ - 81x² - 18x - 2x² + 18x + 4

Rearranging the terms:

x⁴ - 9x³ + 9x³ - 2x² - 2x² - 81x² - 18x + 18x + 4

Simplifying:

x⁴ - 85x² + 4

Any two polynomials can be multiplied in this fashion.

Answer 3

Use the FOIL method - First, Outer, Inner, Last.
(3x+1)(4x+2) = 12x^2 +6x + 4x + 2.
Combine like terms, and you get your answer:
12x^2 + 10x + 2.

Answer 4

First, Outside , Inside and last. Multiply the first two terms in the different parenthesis , so on, so no.
12x^2+6x+4x+2
add like terms together
12x^2+10x+2

Answer 5

you use FOIL
So multiply 3x and 4x
which is 12x^2
then 3x and 2, which is 6x
then 1 and 4x, which is 4x
then 1 and 2, which is 2
so 12x^2+6x+4x+2
combine the similars
12x^2+10x+2

Answer 6

(3x+1)(4x+2) = 3x(4x+2) + 1(4x+2)
= 12x^2 + 6x + 4x + 2
= 12x^2 + 10x +2

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Answer 7

12x^2 + 10x +2

Answer 8

i think of you're maximum suitable in this assumption - you could + & - offering the instruments are a similar ie x^2 subsequently. you could continually examine via substituting a value for x. Say x = 2. so as that would make -12 + fifty six = 40 4 & 11(2^2) = 40 4 examine no remember if it incredibly works for x=3

Answer 9

FOIL = 12x+6x+4x+3, now combine like terms, thats on you man

Answer 10

Hi,

For this question, you need to use the FOIL Method.

First
Outer
Inner
Last

Therefore, here's what you should have once you follow the method:

12x^2 + 10x + 2

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew