how do you multiply?

Question

(5x -6y)(5x+6y)

I came up with 0 is that right? If not what am I doing wrong?

Answer 1

use the identity (a+b)(a-b)=a^2-b^2
(5x-6y)(5x+6y)=25x^2-36y^2

longer method
5x(5x+6y)-6y(5x+6y)
=25x^2+30xy-30xy-36y^2
=25x^2-36y^2

Answer 2

You are not "distributing" one of the factors the right way. It's easier to see if you draw a random box, and divide two adjacent sides into two random sections each. Call one side a+b, and the other one c+d. Draw lines across. The total area is (a+b) times (c+d), but you can see that it is made up of the four pieces ac, bc, ad and bd.

So (5x - 6y) times (5x + 6y) means
(5x - 6y) times 5x, plus (5x - 6y) times 6y.

Now you get 25x^2 - 30xy, plus 30xy - 36y^2, and it makes 25x^2 - 36y^2.

Answer 3

FOIL is a common method, which stands for:
1. first,
2. outer
3. inner
4. last

which is just a way of remembering to multiply all of the terms,

(5x -6y)(5x+6y)

= 25x^2 + 5x6y - 5x6y - 36y^2
first outer inner last

= 25x^2 - 36y^2

Answer 4

I suggest you show how you get 0, then people can better understand what help you need.

And what a FOIL method, which I think is, excuse me, real stupid. Can't it be LOIF, LIOF, FIOL, FLIO, FLOI, etc...??? Why remember the order when it is not necessary? We won't know, someone may failed to do such a question because he can recall the 4 letters but forgot about their order!

I couldn't remember anything about the distributive rule being mentioned until my college maths on group theory. I percieve such rules are for the mathematician to communicate and formulate definitions.

So, like gumballcoolasice3000 suggested, just simply 2x2=4. So, if you have two brackets with m and n terms, which the FOIL method didn't teach you how, you just need to multiply differently a term from each brackets to obtain mn terms.

And, if not sure, just test your method with known numbers. E.g. 9 x 5 = (4+5)(2+3)
So, since 4x2 + 4x3 + 5x2 + 5x3 = 8+12+10+15 = 45 = 9x5, thus method ok.

Answer 5

I do not know how you did, but the answer is
(5x -6y)(5x+6y)=25 x^2 + 30 xy -30xy -36y^2
=25 x^2 -36y^2

Answer 6

(5x -6y)(5x+6y) =
at first 5x * 5X = 25 x^2
then 5X * 6y = 30xy
then -6y * 5x = -30xy
after that -6y * 6y = 36 y^2
and add them up =
25x^2 + 36y^2

That`s it ! I don`t know what you did that you come to 0 !!!!

Answer 7

(5x-6y)(5x+6y)
25X^2+30XY-30XY-36Y^2
( 5 multiply by 5+25 and X by X so X square..5 multltiply by 6=30 and x by y is XY...and so on)

25X^2 -36 Y^2 (30XY- 30XY cancel each other)

(

Answer 8

5x-6y = 0 if and only if 5x=6y.

hmmmmmm...1st time I've heard of FOIL, but it works, don't it?

I learned to multiply by distribution:

(5x-6y)(5x+6y)
=5x(5x+6y)-6x(5x+6y)
=5x*5x+5x*6y-5x*6y-6y*6y
=5x^2-6y*2

Later I learned that (a-b)(a+b)=a^2-b^2 (always),
and you can skip the middle steps, but sometimes I forget to look for this relationship and revert to doing it the long way.

Answer 9

Remember FOIL rule to multiply two binomials...

First+ Outer+ Inner+ Last
=25x^2+30xy-30xy-36y^2
=25x^2-36y^2

Answer 10

Multiply every term by every other term and add.
5x*5x=25x^2
5x*6y=30xy
-6y*5x=-30xy
-6y*6y=-36y^2

25x^2-36y^2

Answer 11

Here is a helpful little mnemonic device
First
Outside
Inside
Last

5x*5x + 5x*6y +.....