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# Factor by grouping examples

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11 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. Read 310 times

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