can someone explain how to multiply binomials and trinomials? please make it simple?

Question

also how to factor an equation

Answer 1

I assume you have heard all of the normal things, like foil, so here is an unconventional way of thinking about it.

Think about it like shaking hands with people at a party.
Let's say "A" walks into a room with "B and C" in it. A and B shake hands and A and C shake hands. B and C don't because they are already at the party together. A(B+C)

What if A has a date with D? Then A and D arrive together.
(A + D)(B + C) Who needs to shake hands? A and B, A and C, D and B, and D and C.

A and D don't need to shake hands, because they aready met. And same thing with B and C.

Same thing holds with trinomials.

It's weird I know, but just remember that numbers are polite and always shake hands with other numbers they meet.

Good luck :)

Answer 2

Okay. The way I was taught to multiply a binomial and a trinomial is with a box.

Let's say you are multiplying this:
(x^2 + x + 1)(x + 1)

What you do is put it in a box. Draw a rectangle that is 4 cells across and 3 cells down. It should have a total of 12 cells (inside boxes).

__________
|__|__|__|__|
|__|__|__|__|
|__|__|__|__|

Across the top row of cells, write the trinomial (the one with the 3 terms). Down the left side of cells, write the binomial (the one with the 2 terms).

____A____B___C__D_
1 |___ |_x^2_|_x_|_1_|
2 |_ x_|____|____|___|
3 |_1_|____|____|___|

Now, all you have to do is multiply like in a multiplication chart. I am going to label the cells with letters and numbers to help you see the placement of the numbers.

Multiply (x^2)(x) When you multiply like terms with exponents, you ADD the exponents. It is known that

x = x^1

1+2=3, so (x^2)(x) = x^3 Place x^3 in cell B2.

Now multiply (x)(x) and you get x^2 Place x^2 in cell C2.

Multiply (x)(1) and you get x Place x in cell D2.

When multiply to get the 3rd row of answers, everything is multiplied times 1, so you can just repeat the trinomial in cells B3, C3, and D3. This is what you get:

____A____B___C__D_
1 |___|_x^2_|_x__|_1_|
2 |_x_|_x^3_|_x^2_|_x_|
3 |_1_|_x^2_|_x__|_1_|

Now, write out the answer, combining like terms. Start with the highest exponent, which is x^3. There is only one, so start your answer as

x^3 +

There are 2 sets of x^2. Adding 1x^2 + 1x^2 = 2x^2.

x^3 + 2x^2 +

There are 2 sets of x. Adding x + x = 2x.

x^3 + 2x^2 + 2x +

Last, there is 1.

x^3 + 2x^2 + 2x + 1

There is your answer.

Hint: If there is a (-) instead of a (+), put it in the box like this:
(x^2 - 2x + 2)(x - 2)

____A____B___C____D_
1 |___ |_x^2_|_-2 x_|_2_|
2 |_x__|____|____|____|
3 |_-2_|____|____|____|

When multiplying, be sure to multiply the negative. For example, when you multiply cell C1 with A3 to get cell C3.

(-2x)(-2) = +4x

Hope that helped.

As for factoring, here is an example:
9x^2 + 12x + 3

The number that can be divided into 9, 12, and 3, is 3. Divide by 3.

3x^2 + 4x + 1

Now, when you CAN NO LONGER divide out numbers, factor it.

( __ + __ )( __ + __ )

When you are multiplying two binomials, you know that the first two terms are multiplied. Knowing this, you know that to get 3, you have to multiply two numbers. Those two numbers MUST be 3 and 1. Since it is 3x^2, you know that an x and another x were multiplied.

( 3x + __ )( x + __ )

Now, to find the other two numbers, look at the last two numbers in the trinomial you are trying to factor. You know that when multiplying two binomials, the last two numbers in each binomial are multiplied to get the last term of the trinomial. You need to find two numbers that multiply to get 1. Of course, it's 1 X 1 = 1

( 3x + 1 )( x + 1)

To check it (this will also tell you how to do FOIL to multiply binomials) simply do FOIL.

F is for FIRST.

(3x)(x) = 3x^2

O is for OUTSIDE.

(3x)(1) = 3x

I is for INSIDE.

(1)(x) = x

L is for LAST.

(1)(1) = 1

Put these terms together and you get:

3x^2 + 3x + x + 1

Now, combine like terms to see if you get the same thing you factored.

You can combine the 3x and the x because they have the same exponent of 1.

3x^2 + 4x + 1

There you have it, mulitplying binomials and trinomials and factoring. Hope I helped. If you have any questions, feel free to contact me by email and I can explain another way to do things. I know more than one way. :D

Answer 3

Take an example
(x+2)(x+1)
FOIL stands for:
Firsts: x and x = x * x = x^2
Outers: x and 1 = x * 1 = x
Inners: 2 and x = 2 * x = 2x
Lasts: 2 and 1 = 2 * 1 = 2

So you'd get: x^2 + x + 2x +2
Then you "combine like terms". So take the "x" (which is 1x) and "2x" and add them to get "3x" and you're done.
Answer x^2 +3x +2

***********************
Example:
(x^2 + 2x + 1)(x^2 + x + 2)
Take each term from the first trinomial (x^2, 2x, and 1) and multiply them each by each term in the other trinomial.
(x^2)(x^2)=x^4
(x^2)(x)=x^3
(x^2)(2)=2x^2

(2x)(x^2)=2x^3
(2x)(x)=2x^2
(2x)(2)=4x

(1)(x^2)=x^2
(1)(x)=x
(1)(2)=2

put them all together: x^4 + x^3 + 2x^2 + 2x^3 + 2x^2 + 4x + x^2 + x + 2

and then combine the like terms to get: x^4 + 3x^3 + 5x^2 + 5x + 2

Honestly at the moment I don't have time to explain factoring, but if you have any questions on what I said or on factoring click my profile and contact me.