SOLUTION: Regarding Products of Sums and Differences Mulitiply and Simplify: (5y+4+3x)(5y+4-3x) 1)is this in the form of (a+b)(a-b)= a^2-b^2? If not, then what form should I use? 2)I

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Regarding Products of Sums and Differences Mulitiply and Simplify: (5y+4+3x)(5y+4-3x) 1)is this in the form of (a+b)(a-b)= a^2-b^2? If not, then what form should I use? 2)I       Log On


   



Question 355702: Regarding Products of Sums and Differences
Mulitiply and Simplify: (5y+4+3x)(5y+4-3x)
1)is this in the form of (a+b)(a-b)= a^2-b^2? If not, then what form should I use?
2)I do not understand how to calculate through the steps of this to get the answer the book says. Can you show me the steps simply but understandably? The answer is 25y^2+40y+16-9x^2. I have tried this many times and NEVER got this answer. I did get the 25y^2 but NEVER the 40y.
I appreciate any help!
Jill

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute.
Let u=5y%2B4 and v=3x
Then %285y%2B4%2B3x%29%285y%2B4-3x%29=%28u%2Bv%29%28u-v%29
%285y%2B4%2B3x%29%285y%2B4-3x%29=u%5E2-v%5E2
.
.
u%5E2=%285y%2B4%29%285y%2B4%29
Use the FOIL Method,
u%5E2=25y%5E2%2B20y%2B20y%2B16
u%5E2=25y%5E2%2B40y%2B16
v%5E2=9x%5E2
.
.
%285y%2B4%2B3x%29%285y%2B4-3x%29=u%5E2-v%5E2
%285y%2B4%2B3x%29%285y%2B4-3x%29=25y%5E2%2B40y%2B16-9x%5E2
%285y%2B4%2B3x%29%285y%2B4-3x%29=25y%5E2%2B40y-9x%5E2%2B16