× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
r
4
L
4
3
d
3
M
3
l
3
V
3
s
3
d
3
a
3
g
3
j
3
New Topic  
Durham_College Durham_College
wrote...
Posts: 3
Rep: 0 0
5 years 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 495 times

Related Topics

New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  1948 People Browsing
Related Images
  
 450
  
 344
  
 4491
Your Opinion
Where do you get your textbooks?
Votes: 447