SOLUTION: Rewrite the expression x^3 - 2x^2 y + x y^2 so that it is easy to calculate the its value without a calculator when x= 21 and y = 19

Question 133324: Rewrite the expression x^3 - 2x^2 y + x y^2 so that it is easy to calculate the its value without a calculator when x= 21 and y = 19
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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

Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient -2? Let's list all of the factors of 1:

Factors of 1:
1

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

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

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

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

From this list we can see that -1 and -1 add up to -2 and multiply to 1

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 )

note: is equivalent to since the term occurs twice. So also factors to

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So our expression goes from and factors further to

So factors to

Plug in x= 21 and y = 19

Subtract

Square 2 to get 4

Multiply

So when x= 21 and y = 19

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