Simplify n(n+1)(2n+1)

Problem

n*(n+1)*(2*n+1)

Solution

1. Distribute the first two terms n and (n+1) to find their product.

n*(n+1)=n2+n

2. Multiply the resulting binomial (n2+n) by the remaining binomial (2*n+1) using the distributive property.

(n2+n)*(2*n+1)=n2*(2*n+1)+n*(2*n+1)

3. Expand each term by distributing the variables across the parentheses.

n2*(2*n+1)=2*n3+n2

n*(2*n+1)=2*n2+n

4. Combine the expanded terms into a single expression.

2*n3+n2+2*n2+n

5. Group like terms to simplify the expression.

2*n3+(1+2)*n2+n

2*n3+3*n2+n

Final Answer

n*(n+1)*(2*n+1)=2*n3+3*n2+n

Want more problems? Check here!