(x+5)(x+6) Expand And Simplify

Jasonbradley

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Jun 16, 2024

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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:

1. 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

2. 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.