SOLUTION: HELLO MAY SOMEONE HELP ME WITH THIS PROBLEM IM STUCK IM HAVING A DIFFICULT TIME IN ALGEBRA. FOIL these polynomials (3x + 5y)(3x - 5y)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: HELLO MAY SOMEONE HELP ME WITH THIS PROBLEM IM STUCK IM HAVING A DIFFICULT TIME IN ALGEBRA. FOIL these polynomials (3x + 5y)(3x - 5y)      Log On


   



Question 149104: HELLO MAY SOMEONE HELP ME WITH THIS PROBLEM IM STUCK IM HAVING A DIFFICULT TIME IN ALGEBRA.
FOIL these polynomials
(3x + 5y)(3x - 5y)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The way I look at it is, each term inside both parentheses gets
multiplied by each term in side the other parenthesis
for practice:
%28a+%2B+b%29%28+c+%2B+d+%2B+e+%2B+f+%2B+g+%2B+h%29
Remember a gets multiplied by EACH term in the other parenthesis
and b also gets multiplied by EACH term in the other parenthesis
ac+%2B+ad+%2B+ae+%2B+af+%2B+ag+%2B+ah
Now for b times the other terms
bc+%2B+bd+%2B+be+%2B+bf+%2B+bg+%2B+bh
The answer is:
ac+%2B+ad+%2B+ae+%2B+af+%2B+ag+%2B+ah+%2B+bc+%2B+bd+%2B+be+%2B+bf+%2B+bg+%2B+bh
Think of your problem as
%28a+%2B+b%29%28c+%2B+d%29
where
a+=+3x
b+=+5y
c+=+3x
d+=+-5y
Following my method,
+%28a+%2B+b%29%28c+%2B+d%29+=+ac+%2B+ad+%2B+bc+%2B+bd
Now just substitute terms
3x%2A3x+%2B+3x%2A%28-5y%29+%2B+5y%2A3x+%2B+5y%2A%28-5y%29
9x%5E2+-+15xy+%2B+15xy+-+25y%5E2
9x%5E2+-+25y%5E2 answer
How can I check this answer? One way is to pick values
for x and y and see if answer checks OK
Let x+=+5
Let y+=+11
%283x+%2B+5y%29%283x+-+5y%29
%283%2A5+%2B+5%2A11%29%283%2A5+-+5%2A11%29
15+%2B+55%29%2815+-+55%29
70%2A%28-40%29+=+-2800
Now check my answer:
9x%5E2+-+25y%5E2
9%2A5%5E2+-+25%2A11%5E2
9%2A25+-+25%2A121
225+-+3025+=+-2800
OK