Let aa and bb be positive integers. Find a+ba+b if a2+a=b4+b3+b2+ba2+a=b4+b3+b2+b.

We are tasked with finding \( a + b \) given that the positive integers \( a \) and \( b \) satisfy the equation:

\[
a^2 + a = b^4 + b^3 + b^2 + b.
\]

### Step 1: Factor both sides

Start by factoring the right-hand side. We observe that the expression \( b^4 + b^3 + b^2 + b \) has a common factor of \( b \):
\[
b^4 + b^3

Let a and b be positive integers. Find a+b if a^2 + a = b^4 + b^3 + b^2 + b.

Learn how to find the sum a + b for positive integers a and b that satisfy the equation a^2 + a = b^4 + b^3 + b^2 + b. This solution covers algebraic concepts such as polynomial equations and factoring techniques. Suitable for students in Grades 9-12.

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