Simplify the expression x^2n+x^(2n+1)+x^(3n+2).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to simplify x^2n + x^(2n+1) + x^(3n+2)

Use the relation x^(a + b) = x^a*x^b

x^2n + x^(2n+1) + x^(3n+2)

=> x^2n + x^2n*x + x^3n*x^2

=> x^2n + x^2n*x + x^2n*x^n*x^2

=> x^2n(1 + x + x^n*x^2)

The simplified form of x^2n + x^(2n+1) + x^(3n+2) is x^2n(1 + x + x^n*x^2)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To simplify the given expression, we'll have to factorize it.

First, we'll write the term x^(2n+1) as it follows:

x^(2n+1) = x^2n*x

We'll re-write the term x^(3n+2);

x^(3n+2) = x^3n*x^2 = x^(2n+n)*x^2 = x^2n*x^n*x^2

We'll re-write the given expression:

x^2n + x^2n*x + x^2n*x^n*x^2

We'll factorize by x^2n:

x^2n*(1 + x + x^n*x^2)

The simplified form of the given expression is: x^2n*(1 + x + x^n*x^2).

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