What is the product of (3x+4) and (x+2)?

Question

my son needs help with math his teacher doesn't explain anything that well so anything helps

Answer 1

When multiplying polynomial like this, the common method is call the FOIL method.

It stands for First, Outer, Inner,Last:

For example

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

a and d are the Outers and b andc are the Inners.

Where a is the first term to be distributed through the second part.

If it was only something like

a(c+d)

then you would distribute a through (c+d) giving ac + ad. Remember the rule for multiplication over addition.

----

Another way to look at it is:

(a+b)(c+d) is the same as a(c+d) + b(c+d).

For this case 3x is a, b is 4, c is x and 2 is d.

So it would be 3x(x+2) + 4(x+2) = 3x²+6x + 4x + 8. 6x and 4x can be combined to make 10x.

The final answer is 3x²+10x+8

Answer 2

You can imagine this as a question of the addition of (3x+4)*x and (3x+4)*2

(3x+4)*x = 3x²+4x

(3x+4)*2 = 6x+8

Add them together:

3x²+4x+6x+8 = 3x²+10x+8

(3x+4)(x+2) = 3x²+10x+8

Answer 3

Hello, Tommy,

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

This type of problem is solved by a method termed “F.O.I.L.,” which stands for First, Outer, Inner, Last.

First multiply the two first terms in each () section: 3x*x = 3x²

Next, multiply the two Outer terms together: 3x*2 = 6x

Third, multiply the two Inner terms together: 4*x = 4x

Finally, multiply the two Last terms: 4/*2 = 8

Sum all these terms and combine, where possible:

3x² + 6x + 4x + 8 = 3x² + 10x + 8

The answer is 3x² + 10x + 8.

I hope this helps,

Bob