How do you factor #(x+1)^(3/2) + (x+1)^(1/2)#?

1 Answer
Nov 27, 2015

Answer:

#(x+1)^(1/2)(x+2)#

Explanation:

#(x+1)^(3/2) +(x+1)^(1/2)#

Re-write using exponential rule

Remember #color(red)(x^n*x^m = x^(m+n)#

Let's rewrite #(color(red)(x+1))^(2/2)(x+1)^(1/2) + 1(x+1)^(1/2)#

#=> (x+1)^(1/2)(color(red)[(x+1)^(2/2)+1})#

#=> (x+1)^(1/2)(x+1+1)#; remember #2/2=1#

Answer : #=> (x+1)^(1/2)(x+2)#