Expanding and Simplifying (x + 5)(x + 6)
This article will walk you through the process of expanding and simplifying the expression (x + 5)(x + 6). This is a fundamental skill in algebra that involves the distributive property and combining like terms.
The Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In this case, we can apply the distributive property twice:

First distribution:
 Multiply the first term in the first set of parentheses (x) by both terms in the second set of parentheses (x and 6). This gives us: x(x + 6) = x² + 6x

Second distribution:
 Multiply the second term in the first set of parentheses (5) by both terms in the second set of parentheses (x and 6). This gives us: 5(x + 6) = 5x + 30
Combining Like Terms
Now we have: x² + 6x + 5x + 30
Notice that 6x and 5x are like terms, meaning they both have the same variable raised to the same power. We can combine them:
x² + 11x + 30
The Final Answer
Therefore, the expanded and simplified form of (x + 5)(x + 6) is x² + 11x + 30.
This process can be generalized to any two binomials. Remember to apply the distributive property and then combine like terms.