SOLUTION: Regarding Products of Sums and Differences Multiply and Simplify (2t+3)^2 - (t-1)(t+1) Please show me the steps to solving this. What form is used? How do I know what to do

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Regarding Products of Sums and Differences Multiply and Simplify (2t+3)^2 - (t-1)(t+1) Please show me the steps to solving this. What form is used? How do I know what to do      Log On


   

Question 355708: Regarding Products of Sums and Differences
Multiply and Simplify (2t+3)^2 - (t-1)(t+1)
Please show me the steps to solving this.
What form is used?
How do I know what to do first?
Thank you,
Jill
Found 2 solutions by Fombitz, mananth:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Doesn't matter which you do first, you should get the same answer.
Use the FOIL method for both.
%282t%2B3%29%282t%2B3%29=4t%5E2%2B6t%2B6t%2B9
%282t%2B3%29%5E2=4t%5E2%2B12t%2B9
.
.
.
%28t-1%29%28t%2B1%29=t%5E2%2Bt-t-1
%28t-1%29%28t%2B1%29=t%5E2-1
.
.
.
%282t%2B3%29%5E2+-+%28t-1%29%28t%2B1%29=%284t%5E2%2B12t%2B9%29-%28t%5E2-1%29
%282t%2B3%29%5E2+-+%28t-1%29%28t%2B1%29=4t%5E2%2B12t%2B9-t%5E2%2B1
%282t%2B3%29%5E2+-+%28t-1%29%28t%2B1%29=highlight%283t%5E2%2B12t%2B10%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(2t+3)^2 - (t-1)(t+1)

(2t+3)^2-(t^2-1) .............( (a+b)(a-b)= a^2-b^2) here a =t & b =1)
(4t^2+12t+9)-(t^2-1)...........( (a+b)^2 = a^2+2ab+b^2; a= 2t and b =3)
4t^2+12t+9-t^2+1
group the similar terms & simplify
4t^2-t^2+12t+9+1
3t^2+12t+10
...
In such problems first solve the terms in the brackets and then simplify
..
m.ananth@hotmail.ca