SOLUTION: Factor and check: x^2 - 3xy

SOLUTION: Factor and check: x^2 - 3xy - 4y^2

Question 146173This question is from textbook
: Factor and check: x^2 - 3xy - 4y^2 This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -4 respectively.

Now multiply the first coefficient 1 and the last coefficient -4 to get -4. Now what two numbers multiply to -4 and add to the middle coefficient -3? Let's list all of the factors of -4:

Factors of -4:
1,2

-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -4
(1)*(-4)
(-1)*(4)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

First Number	Second Number	Sum
1	-4	1+(-4)=-3
-1	4	-1+4=3

From this list we can see that 1 and -4 add up to -3 and multiply to -4

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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Answer:
So factors to

Check:

In order to check our answer, we need to FOIL

Remember, when you FOIL an expression, you follow this procedure:

Multiply the First terms:.

Multiply the Outer terms:.

Multiply the Inner terms:.

Multiply the Last terms:.

Now collect every term to make a single expression.

Now combine like terms.

So FOILS to .

In other words, .

So this verifies our answer.