Directions:Multiply

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

so the answer for it i got:

((20x^2+20x-36)/(80))

I worked it and I have what you have EXCEPT 29x instead of 20x. If you can't find the error, post your work and we can help you find it.

PLEASE HELP ME FIND MY ERROR....THIS IS WHAT I DID.

Directions:Multiply

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

The steps i took:
First i simplify between (x)/(3) and (3)/(4) the common denominator is 12.
Then multiplied: x(4) and 3(3)= ((4x+9)/(12))

between (3x)/(4) and (3)/(5) the common denominator is 20.

so then i multiplied: 3x(5) and 3(4)=
(15x-12)/(20)

Now i have:((4x+9)/(12))((15x-12)/(20))

NOw i multiplied: ((4x+9)(15x)/(240))

now i factored out a 3 out of the top to get:
3((4x+9)(5x-4)/(240))
now i simplify again:
((4x+9)(5x-4)/80)

now foil the top:
f=4x(5x)
o=4x(-4)
i=9(5x)
l=9(-4)

(4x+9)(5x-4)
=4x(5x)+4x(-4)+9(5x)+9(-4)
=20x^2-16x+45x-36
=20x^2+20x-36

NOW i just put that back in:

((4x+9)(5x-4)/(80))

so that's how i came up with:
((20x^2+20x-36)/(80))

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

The steps i took:
First i simplify between (x)/(3) and (3)/(4) the common denominator is 12.
Then multiplied: x(4) and 3(3)= ((4x+9)/(12))

between (3x)/(4) and (3)/(5) the common denominator is 20.

so then i multiplied: 3x(5) and 3(4)=
(15x-12)/(20)

Now i have:((4x+9)/(12))((15x-12)/(20))ok to here.

NOw i multiplied: ((4x+9)(15x-12)/(240))
you dropped the -12
now i factored out a 3 out of the top to get:
3((4x+9)(5x-4)/(240))
now i simplify again:
((4x+9)(5x-4)/80)

now foil the top:
f=4x(5x)
o=4x(-4)
i=9(5x)
l=9(-4)

(4x+9)(5x-4)
=4x(5x)+4x(-4)+9(5x)+9(-4)
=20x^2-16x+45x-36
=20x^2+20x-36

OKAY I DON'T SEE IT CAN YOU EXPLAIN TO ME WHAT AM I SUPPOST TO DO.OR WHAT SHOULD IT LOOK LIKE

NOw i multiplied: ((4x+9)(15x-12)/(240))
you dropped the -12.
(4x+9)(15x-12)/240 =
FOIL it.
(60x^2 -48x +135x -108)/240 =
Combine terms.
(60x^2 + 87x -108)/240 =
Divide by 3.
(20x^2 + 29x -36)/80 =

I don't know how your are to leave it in final form but I'm sure you can take it from here.
now i factored out a 3 out of the top to get:
3((4x+9)(5x-4)/(240))
now i simplify again:
((4x+9)(5x-4)/80)

now foil the top:
f=4x(5x)
o=4x(-4)
i=9(5x)
l=9(-4)

(4x+9)(5x-4)
=4x(5x)+4x(-4)+9(5x)+9(-4)
=20x^2-16x+45x-36
=20x^2+20x-36

I appreciate all your help....especially correcting my wrongness.

No problem! I'm glad I could help. It's common to make mistakes while solving mathematical problems, so it's always good to double-check your work.

In this case, the mistake was in the step where you multiplied ((4x+9)(15x-12)/(240)). You accidentally dropped the -12 term.

To correct it, you need to perform the multiplication correctly. Let's go through the steps again:

((4x+9)(15x-12)/(240))

Multiply using the FOIL method:
= (4x * 15x) + (4x * -12) + (9 * 15x) + (9 * -12)
= (60x^2) + (-48x) + (135x) + (-108)

Combine like terms:
= 60x^2 + 87x - 108

Now, you need to simplify this expression. Since the numerator and denominator both have a common factor of 3, you can factor it out:
= 3(20x^2 + 29x - 36)

Finally, divide both the numerator and denominator by 80 to simplify further:
= (20x^2 + 29x - 36) / 80

So, the correct answer is ((20x^2 + 29x - 36) / 80).