Ask a Question
  
  
  
Top Posters
Since Sunday
7
5
4
4
4
4
4
4
4
4
4
4
New Topic  
wrote...
Posts: 1
Rep: 0 0
4 months ago
#9:   \(x^2+y^2+2xy-4\)

Rearrange

\(x^2+2xy+y^2-4\)

Factor the first three terms as your would a quadratic trinomial by trial and error \(\left(x^2+2xy+y^2\right)-4\). It becomes:

\(\left(x+y\right)\left(x+y\right)-4\)

Write the brackets in exponent form:

\(\left(x+y\right)^2-4\)

This is a difference of squares, so use the pattern: \(a^2-b^2=\left(a+b\right)\left(a-b\right)\)

\(a=x+y\)
\(b=2\) because the square root of \(4\) is \(2\)

Therefore:

\(\left(x+y+2\right)\left(x+y-2\right)\)



#11:   \(m^2-n^2-4+4n\)

Rearrange like this, notice how I grouped them as a trinomial and factored out the negative:

\(m^2-\left(n^2-4n+4\right)\)

Now factor by trial and error:

\(m^2-\left[\left(n-2\right)\left(n-2\right)\right]\)

Write as an exponent:

\(m^2-\left(n-2\right)^2\)

This is a difference of squares:

\(\left(m-\left(n-2\right)\right)\left(m+\left(n-2\right)\right)\)

Clean up more:

\(\left(m-n+2\right)\left(m+n-2\right)\)
Source  Calter, Michael A., Paul Calter, Paul Wraight, Sarah White. Technical Mathematics with Calculus, Canadian Edition, 3rd Edition. John Wiley & Sons (Canada), 2016.
Read 197 times
Related Topics
New Topic      
Hold tight!  A Bio Forums Expert has been contacted to start answering this thread.
Explore
Post your homework questions and get free online help from our incredible volunteers.
Learn More
Improve Grades
Help Others
Save Time
Accessible 24/7
  146 People Browsing
 125 Signed Up Today
Related Images
 1093
 121
 43
Your Opinion
What type of music do you study to?
Votes: 41