SOLUTION: Perform the indicated operation (2b +3)(5b-1)-(b + 2)^2

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Question 150454: Perform the indicated operation

(2b +3)(5b-1)-(b + 2)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2 Start with the given expression.


%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%5E2 FOIL %282b+%2B3%29%285b-1%29 to get %282b+%2B3%29%285b-1%29=10b%5E2-2b%2B15b-3=10b%5E2%2B13b-3


%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%28b+%2B+2%29 Expand %28b+%2B+2%29%5E2 to get %28b+%2B+2%29%28b+%2B+2%29


%2810b%5E2%2B13b-3%29-%28b%5E2%2B4b%2B4%29 FOIL %28b+%2B+2%29%28b+%2B+2%29 to get %28b+%2B+2%29%28b+%2B+2%29=b%5E2%2B2b%2B2b%2B4=b%5E2%2B4b%2B4


10b%5E2%2B13b-3-b%5E2-4b-4%29 Distribute the negative. Think of -%28b%5E2%2B4b%2B4%29 as -1%28b%5E2%2B4b%2B4%29


%2810b%5E2-b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29 Group like terms. Make sure that each group is separated by a "+" sign.


%289b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29 Subtract b%5E2 from 10b%5E2 to get 9b%5E2


%289b%5E2%29%2B%289b%29%2B%28-3-4%29 Subtract 4b from 13b to get 9b


%289b%5E2%29%2B%289b%29%2B%28-7%29 Subtract 4 from -3 to get -7


9b%5E2%2B9b-7 Remove the parenthesis.


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Answer:


So %282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2 simplifies to 9b%5E2%2B9b-7

In other words, %282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2=9b%5E2%2B9b-7