# FOIL confusion: (x - 7)(x + 10), (3r + 9)(2r - 1), etc

#### val24

##### New member
Hello, i am experiencing all kinds of confusion as far as FOIL goes. I understand the concept, and I got the first bunch of questions right aka

(x - 7) (x + 10)
x^2 + 10x - 7X + 70
x^2 + 3x + 70

but then I am encountering ones like (3r + 9) (2r - 1) and i did
(3r + 9) (2r - 1)
6r^2 + 3r - 18r - 1
6r^2 + -15r - 1

... but the answer says 6r^2 + 15r - 1 (without the negative). Wouldn't it have to be 18r - 3r to be a non-negative 15? Also I am confused as to when to put a plus sign and when to put a minus sign. We are also doing solving linear equations and when I am attempting to balance the sides, I am just randomly choosing a plus or a minus sign sometimes to be honest. Because I just have no idea.

Also, a lot of the advance questions on this sheet... I have no idea how to attempt. Such as these ones (instructions say Expand and simplify)
(a - 4) (a - 6) + 5(3a - 2) [What do I do with the second part.. with the 5?]
(x + 5)(x - 3) + (x - 4)(x + 2) [Do I do the one side and then the other and then simplify them together?]

And this one here (the instructions above say Simplify by first expanding binomials)
4(x + 6)(x - 4) [I really just have no idea on this one... what do i do with that 4?]

Sorry that this is a bit long. I'm just really confused.

#### Mrspi

##### Senior Member
Re: FOIL confusion

val24 said:
Hello, i am experiencing all kinds of confusion as far as FOIL goes. I understand the concept, and I got the first bunch of questions right aka

(x - 7) (x + 10)
x^2 + 10x - 7X + 70
x^2 + 3x + 70

but then I am encountering ones like (3r + 9) (2r - 1) and i did
(3r + 9) (2r - 1)
6r^2 + 3r - 18r - 1
6r^2 + -15r - 1

... but the answer says 6r^2 + 15r - 1 (without the negative). Wouldn't it have to be 18r - 3r to be a non-negative 15? Also I am confused as to when to put a plus sign and when to put a minus sign. We are also doing solving linear equations and when I am attempting to balance the sides, I am just randomly choosing a plus or a minus sign sometimes to be honest. Because I just have no idea.
Please be VERY careful on your multiplication:

(3r + 9)(2r - 1)
3r*2r + 3r*(-1) + 9*(2r) + 9*(-1)
6r[sup:36ky3tif]2[/sup:36ky3tif] - 3r + 18r + (-9)
6r[sup:36ky3tif]2[/sup:36ky3tif] + 15r - 9

I think you have made a SIGN error.

Also, a lot of the advance questions on this sheet... I have no idea how to attempt. Such as these ones (instructions say Expand and simplify)
(a - 4) (a - 6) + 5(3a - 2) [What do I do with the second part.. with the 5?]
Yes...multiply the (a - 4)(a - 6), and multiply 5(3a - 2):

a*a - a*6 - 4*a - 4(-6) + 5*3a + 5*(-2)

a[sup:36ky3tif]2[/sup:36ky3tif] - 6a - 4a + 24 - 15a - 10

Combine like terms.

(x + 5)(x - 3) + (x - 4)(x + 2) [Do I do the one side and then the other and then simplify them together?]
Basically yes...
(x + 5)*(x - 3) is x*x - 3*x + 5*x + 5*(-3), or x[sup:36ky3tif]2[/sup:36ky3tif] + 2x - 15
(x - 4)(x + 2) is x*x + x*2 - 4*x - 4*2, or x[sup:36ky3tif]2[/sup:36ky3tif] - 2x - 8

Combining the two products gives you this:

x[sup:36ky3tif]2[/sup:36ky3tif] + 2x - 15 + x[sup:36ky3tif]2[/sup:36ky3tif] - 2x - 8
Combine like terms.....

And this one here (the instructions above say Simplify by first expanding binomials)
4(x + 6)(x - 4) [I really just have no idea on this one... what do i do with that 4?]
You can multiply the two binomials first:

4(x + 6)(x - 4)
4[ x*x - x*4 + 6*x + 6*(-4)]
4[ x[sup:36ky3tif]2[/sup:36ky3tif] - 4x + 6x - 24]
4[x[sup:36ky3tif]2[/sup:36ky3tif] + 2x - 24 ]
Now...multiply each term inside the square brackets by 4.
Sorry that this is a bit long. I'm just really confused.

#### Loren

##### Senior Member
Re: FOIL confusion

(x - 7) (x + 10)
x^2 + 10x - 7X + 70 <<< should be -70.
x^2 + 3x + 70