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6 years ago
#9:   x2+y2+2xy−4

Rearrange

x2+2xy+y2−4

Factor the first three terms as your would a quadratic trinomial by trial and error (x2+2xy+y2)−4. It becomes:

(x+y)(x+y)−4

Write the brackets in exponent form:

(x+y)2−4

This is a difference of squares, so use the pattern: a2−b2=(a+b)(a−b)

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

Therefore:

(x+y+2)(x+y−2)


#11:   m2−n2−4+4n

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

m2−(n2−4n+4)

Now factor by trial and error:

m2−[(n−2)(n−2)]

Write as an exponent:

m2−(n−2)2

This is a difference of squares:

(m−(n−2))(m+(n−2))

Clean up more:

(m−n+2)(m+n−2)
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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