problem with multiplying polynomials

PixelZombie

New member
Joined
Feb 6, 2009
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6
i am using the foil method and i know my answers wrong


[5+(x-y)][5-(x-y)]

here's what I got

25-5x-5y+5x-5y-(x-y)(x-y) i think i didn't something wrong here
25-10y-(x-y)(x-y)
25-10y-x^-xy-xy+y^
25-10y-x^+xy^+y^ do you add 10y to y^ and if so then 10y+y^=10 cubed?

sorry to ask so many questions, I don't have my algebra book yet.
 
Hello, PixelZombie!

[5+(xy)][5(xy)]\displaystyle \bigg[5+(x-y)\bigg]\,\bigg[5-(x-y)\bigg]

Here's what I got

. . 255(xy)+5(xy)These cancel!(xy)(xy)\displaystyle 25-\underbrace{5(x-y)+5(x-y)}_{\text{These cancel!}}-(x-y)(x-y)

So we have: .25(x22xy+y2)  =  25x2+2xyy2\displaystyle 25 - (x^2 - 2xy + y^2) \;=\;25 - x^2 + 2xy - y^2

 
do you multiply 5 to 5-(x-Y) or 5 to (x-Y)?

i am sorry but can you illustrate lol
this is really confusing...
 
PixelZombie said:
i am using the foil method and i know my answers wrong


[5+(x-y)][5-(x-y)]

here's what I got

25-5x-5y+5x-5y-(x-y)(x-y) i think i didn't something wrong here
25-10y-(x-y)(x-y)
25-10y-x^-xy-xy+y^
25-10y-x^+xy^+y^ do you add 10y to y^ and if so then 10y+y^=10 cubed?

sorry to ask so many questions, I don't have my algebra book yet.

Do you see that your complicated-looking multiplication is really of the form (a + b)(a - b)?

In your multiplication, a = 5, and b = (x - y)....so your multiplication of {5 + (x - y)]*[5 - (x - y)] is of that form.

The product of the sum and the difference of the same two numbers is the difference of the squares of those numbers:

(a + b)(a - b) = a^2 - b^2

If you're not SURE that is true, multiply out (a + b)(a - b) and see what you get!

So....

In your problem, a = 5, and b = x - y.

So,

a^2 - b^2 = 5^2 - (x - y)^2

Do the squaring:

25 - (x - y)(x - y)

I'll let YOU do the last part!
 
ok

[5+(x-y)][5-(x-y)]

25-5x-5y+5x-5y-(x-y)(x-y)

25-5x-5y+5x-5y-x^2+2xy+y^2

turns out to be 25-10y-x^2+2xy+y^2

i see how 5x crosses each other out,(-5x+5x) but what about 5y?
(-5y+-5y) equals? 10y

show me where i am wrong so that I can make corrections.
 
PixelZombie said:
[5+(x-y)][5-(x-y)]
25-5x-5y+5x-5y-(x-y)(x-y)
NO!
Start by getting rid of inside brackets:
(5 + x - y)(5 - x + y)
Now perform the multiplication.
 
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