(m%2B9).jpeg "(3m+1)(m+9)")
Expanding the Expression (3m+1)(m+9)
This article will guide you through the process of expanding the expression (3m+1)(m+9), demonstrating the application of the distributive property.
Understanding 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 algebraic terms, this is represented as: a(b+c) = ab + ac
Applying the Distributive Property
To expand the expression (3m+1)(m+9), we will use the distributive property twice:
-
Distribute (3m+1) over (m+9): (3m+1)(m+9) = (3m+1)*m + (3m+1)*9
-
Distribute again: (3m+1)m + (3m+1)9 = 3mm + 1m + 3m9 + 19
-
Simplify: 3mm + 1m + 3m9 + 19 = 3m² + m + 27m + 9
-
Combine like terms: 3m² + m + 27m + 9 = 3m² + 28m + 9
Therefore, the expanded form of (3m+1)(m+9) is 3m² + 28m + 9.
Conclusion
By applying the distributive property, we have successfully expanded the given expression. This process is crucial in simplifying and manipulating algebraic expressions, enabling us to solve equations and analyze relationships between variables. Remember, understanding the distributive property is fundamental for mastering algebraic operations.