SOLUTION: how would i factor (x + 2y) squared - 3(x+2y) +2

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Question 253891: how would i factor (x + 2y) squared - 3(x+2y) +2

Found 3 solutions by stanbon, richwmiller, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how would i factor (x + 2y) squared - 3(x+2y) +2
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You have a quadratic with x+2y being the variable.
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Let x+2y = w
Substitute to get:
w^2 - 3w + 2
(w-2)(w-1)
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Substitute back to get the final factored form:
(x+2y-2)(x+2y-1)
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Cheers,
Stan H.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
And that works out to:
(x+2y)^2-3(x+2y)+2
multiply that out to get
x^2+4xy-3x+4y^2-6y+2
factor that to get
(x+2y-2)(x+2y-1)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+%2B+2y%29%5E2-3%28x%2B2y%29%2B2 Start with the given expression.


Let z=x%2B2y


z%5E2-3z%2B2 Replace x%2B2y with 'z'


Looking at the expression z%5E2-3z%2B2, we can see that the first coefficient is 1, the second coefficient is -3, and the last term is 2.


Now multiply the first coefficient 1 by the last term 2 to get %281%29%282%29=2.


Now the question is: what two whole numbers multiply to 2 (the previous product) and add to the second coefficient -3?


To find these two numbers, we need to list all of the factors of 2 (the previous product).


Factors of 2:
1,2
-1,-2


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 2.
1*2 = 2
(-1)*(-2) = 2

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -3:


First NumberSecond NumberSum
121+2=3
-1-2-1+(-2)=-3



From the table, we can see that the two numbers -1 and -2 add to -3 (the middle coefficient).


So the two numbers -1 and -2 both multiply to 2 and add to -3


Now replace the middle term -3z with -z-2z. Remember, -1 and -2 add to -3. So this shows us that -z-2z=-3z.


z%5E2%2Bhighlight%28-z-2z%29%2B2 Replace the second term -3z with -z-2z.


%28z%5E2-z%29%2B%28-2z%2B2%29 Group the terms into two pairs.


z%28z-1%29%2B%28-2z%2B2%29 Factor out the GCF z from the first group.


z%28z-1%29-2%28z-1%29 Factor out 2 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28z-2%29%28z-1%29 Combine like terms. Or factor out the common term z-1


%28x%2B2y-2%29%28x%2B2y-1%29 Plug in z=x%2B2y

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Answer:


So %28x+%2B+2y%29%5E2-3%28x%2B2y%29%2B2 factors to %28x%2B2y-2%29%28x%2B2y-1%29.


In other words, %28x+%2B+2y%29%5E2-3%28x%2B2y%29%2B2=%28x%2B2y-2%29%28x%2B2y-1%29.