9%2B5(5m%2B3).jpeg "(2m+1)9+5(5m+3)")
Simplifying Algebraic Expressions: (2m+1)9 + 5(5m+3)
This article will guide you through simplifying the algebraic expression (2m+1)9 + 5(5m+3). We'll break down the steps using the distributive property and combining like terms.
Understanding the Expression
The expression consists of two parts:
- (2m+1)9: This part involves multiplying the entire term (2m+1) by 9.
- 5(5m+3): Here, we multiply the entire term (5m+3) by 5.
Using 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.
Applying this to our expression:
- (2m+1)9 = (2m * 9) + (1 * 9) = 18m + 9
- 5(5m+3) = (5 * 5m) + (5 * 3) = 25m + 15
Combining Like Terms
Now, our expression looks like this: 18m + 9 + 25m + 15
We can combine the terms with 'm' and the constant terms separately:
- 18m + 25m = 43m
- 9 + 15 = 24
Simplified Expression
Finally, combining the results, we get the simplified expression:
43m + 24
Conclusion
Therefore, the simplified form of the algebraic expression (2m+1)9 + 5(5m+3) is 43m + 24. By applying the distributive property and combining like terms, we successfully simplified the expression.