Questions: Multiply and collect like terms: (n+1)(n-6).

Transcript text: Multiply and collect like terms: $(n+1)(n-6)$.

Solution

Solution Steps

To solve the problem of multiplying and collecting like terms for the expression $(n+1)(n-6)$, we will use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

Step 1: Expand the Expression

We start with the expression $(n + 1)(n - 6)$. Using the distributive property, we multiply each term in the first binomial by each term in the second binomial:

\[ (n + 1)(n - 6) = n \cdot n + n \cdot (-6) + 1 \cdot n + 1 \cdot (-6) \]

Step 2: Combine Like Terms

Now, we simplify the expression by combining like terms:

\[ n^2 - 6n + n - 6 = n^2 - 5n - 6 \]