What is the difference between squaring #sqrt(x-1)# and #sqrtx -1#?

1 Answer
sente
Dec 22, 2016

#(sqrt(x-1))^2 = x-1#

#(sqrt(x)-1)^2 =x-2sqrt(x)+1#

Explanation:

Notice that #sqrt(x-1)# is a single term, whereas #sqrt(x)-1# has two terms. When we square #sqrt(x)-1#, then, we need to use the distributive property when multiplying, unlike when squaring #sqrt(x-1)#.

#(sqrt(x-1))^2 = sqrt(x-1)*sqrt(x-1) = x-1#

#(sqrt(x)-1)^2 = (sqrt(x)-1)(sqrt(x)-1)#

#= sqrt(x) * sqrt(x)+sqrt(x)*(-1)+(-1)*sqrt(x)+(-1)(-1)#

#=x-2sqrt(x)+1#

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