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

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Answer 1 · 2015-11-27T22:41:29

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

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

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 : $=> (x+1)^(1/2)(x+2)$

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