# How do you Multiply this?

(x/3+3/4)(3x/4-3/5)

## know I am supposed to use the FOIL method.But is this right? I am really not sure I did this right, something just seems off about it.

So i would Multiply
x/3 * 3x/4=x^2/4
x/3 *-3/5= -x/5
3/4 *3x/4=9x/4
3/4 * -3/5
I know to add both of my bottom numbers have to be the same so the common factors of them would be 20
so I get x^2-4x/20+45x/20-9/20=
x^2+41x/20-9/20

## know I am supposed to use the FOIL method.But is this right? I am really not sure I did this right, something just seems off about it.

So i would Multiply
x/3 * 3x/4=x^2/4
x/3 *-3/5= -x/5
3/4 *3x/4=9x/4 wouldn't this be 9x/16?

3/4 * -3/5
I know to add both of my bottom numbers have to be the same so the common factors of them would be 20
so I get x^2-4x/20+45x/20-9/20=
x^2+41x/20-9/20

## What happened to the 4 (x^2/4) from the first term? You started with that but I think your dropped it.

For the middle term, it is -x/5 + 9x/16 and that part becomes (-16x + 45x)/80 which is 29x/80.

The last term is 9/20.

Then you can get rid of the 4, 80, and 20 as denominators by multiplying through by 80.

Check my thinking. Check my arithmetic.

## To multiply the given expression (x/3 + 3/4)(3x/4 - 3/5), you can use the FOIL method. FOIL stands for First, Outer, Inner, Last, which are the steps you'll follow to multiply the two binomials.

1. First: Multiply the first terms of each binomial.
(x/3) * (3x/4) = (3x^2)/(3*4) = (3x^2)/12 = x^2/4

2. Outer: Multiply the outer terms of each binomial.
(x/3) * (-3/5) = (-3x)/15 = -x/5

3. Inner: Multiply the inner terms of each binomial.
(3/4) * (3x/4) = (9x)/(4*4) = (9x)/16

4. Last: Multiply the last terms of each binomial.
(3/4) * (-3/5) = (-9)/(4*5) = (-9)/20

Now, combine all the products obtained:
(x/3 + 3/4)(3x/4 - 3/5) = (x^2/4) + (-x/5) + (9x/16) + (-9/20)

To simplify this expression further, you can find a common denominator and then combine like terms.