How do you factor #r^2-4r+4#?

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Answer 1 · 2016-05-10T06:12:02

#color(blue)( (r - 2 ) ( r - 2) # is the factorised form of the expression.

#r^2 - 4r + 4#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ar^2 + br + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*4 = 4#

AND

#N_1 +N_2 = b = -4#

After trying out a few numbers we get #N_1 = -2# and #N_2 =-2#

#( - 2) *(-2) = 4 #, and #(-2 ) +( - 2)= - 4 #

#r^2 color(blue)(- 4r) + 4 = r^2 color(blue)(- 2r - 2r) + 4#

#= r ( r - 2)- 2 ( r - 2 )#

#= (r - 2 ) ( r - 2) #