SOLUTION: Write the resulting polynomial in standard form. [(x+1)-y]^2

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Question 347518: Write the resulting polynomial in standard form. [(x+1)-y]^2
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

There's a short way and a long way to do this.

The short way depends on
The key is understanding that in the pattern for , the "a" and the "b" can be any expression. We just need two expressions being subtracted!

In your expression, you have two expressions being subtracted: (x+1) and y. SO we can use the pattern replacing "a" with (x+1) and "b" with y:

(Note: If you cannot "see" how this was done, then perhaps the use of a temporary variable will help. Let q = (x+1). Substituting q for (x+1) in your expression we get . It should be obvious how this fits the pattern for : . Now that we are finished using q to help us see how to use the pattern, we just replace the q with (x+1) giving: (which is the same as the expression we got without using the temporary variable, q.)

Now we can use the pattern for on the first part of the above:

Continuing to simplify:


Last of all we put it in standard form:


The long way is to actually square your expression:


To multiply polynomials we multiply each term of one polynomial by each term of the other polynomial. Since there are 3 terms in each of the polynomials there will be 3*3 or 9 multiplications:

Now we simplify:


And now standard form:

The is the same as we got the short way.
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