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

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

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)   (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)   (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)   (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Let

Replace with 'z'

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

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

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

Factors of :
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 .
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 :

First Number Second Number Sum
1 2 1+2=3
-1 -2 -1+(-2)=-3

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

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out 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.

Combine like terms. Or factor out the common term

Plug in

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Answer:

So factors to .

In other words, .