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Factor by grouping examples
Durham_College
Durham_College
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4 months ago
Factor by grouping examples
#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.
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