Additional Tips and Tricks

Oct 13, 2025 by talynt.org 82 views

Introduction

In this article, we will simplify the given expression: 4(1 + 7m) + 4m. This involves applying the distributive property and combining like terms to arrive at a simplified expression. We will break down the steps involved in simplifying the expression and provide a clear explanation of each step.

Step 1: Apply the Distributive Property

The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac. We can apply this property to the given expression by distributing the 4 to the terms inside the parentheses.

4(1 + 7m) = 4(1) + 4(7m)

Using the distributive property, we can rewrite the expression as:

4(1 + 7m) = 4 + 28m

Step 2: Combine Like Terms

Now that we have applied the distributive property, we can combine like terms. In this case, we have two terms: 4 and 28m. Since they are like terms, we can combine them by adding their coefficients.

4 + 28m = 4 + 28m

However, we can simplify this expression further by combining the constant term with the variable term.

4 + 28m = 4(1 + 7m)

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by rewriting it in a more compact form.

4(1 + 7m) + 4m = 4(1 + 7m) + 4m

Using the distributive property, we can rewrite the expression as:

4(1 + 7m) + 4m = 4 + 28m + 4m

Combining like terms, we get:

4 + 28m + 4m = 4 + 32m

Conclusion

In this article, we simplified the expression 4(1 + 7m) + 4m by applying the distributive property and combining like terms. We broke down the steps involved in simplifying the expression and provided a clear explanation of each step. By following these steps, we arrived at a simplified expression: 4 + 32m.

Final Answer

The final answer is: $\boxed{4 + 32m}$

Additional Tips and Tricks

When simplifying expressions, it's essential to apply the distributive property and combine like terms.
Use the distributive property to rewrite expressions in a more compact form.
Combine like terms by adding their coefficients.
Simplify expressions by rewriting them in a more compact form.

Common Mistakes to Avoid

Failing to apply the distributive property when simplifying expressions.
Not combining like terms when simplifying expressions.
Rewriting expressions in a more compact form without applying the distributive property.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics, and it has numerous real-world applications. For example, in physics, simplifying expressions is essential for solving problems involving motion, energy, and momentum. In engineering, simplifying expressions is crucial for designing and optimizing systems.

Conclusion

In conclusion, simplifying expressions is a fundamental concept in mathematics that has numerous real-world applications. By applying the distributive property and combining like terms, we can simplify expressions and arrive at a more compact form. This article provided a step-by-step guide on how to simplify the expression 4(1 + 7m) + 4m, and we arrived at a simplified expression: 4 + 32m.