7(g−10h+4)

OP Authors 2025

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16-03-2025

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Unpacking the Expression: 7(g - 10h + 4)

The expression 7(g - 10h + 4) might look intimidating at first glance, but it's a simple case of applying the distributive property of multiplication. Let's break it down step-by-step to understand what it means and how to simplify it.

Understanding the Distributive Property

The distributive property states that multiplying a number by a sum or difference is the same as multiplying the number by each term in the sum or difference and then adding or subtracting the results. In simpler terms:

a(b + c) = ab + ac

and similarly:

a(b - c) = ab - ac

In our expression, 7(g - 10h + 4), the 'a' is 7, and the terms inside the parentheses (g, -10h, and 4) are 'b', 'c', and 'd' respectively, even though we have three terms instead of two. The distributive property still applies.

Applying the Distributive Property

To simplify 7(g - 10h + 4), we multiply 7 by each term within the parentheses:

• 7 * g = 7g
• 7 * (-10h) = -70h
• 7 * 4 = 28

The Simplified Expression

Putting these results together, we get the simplified expression:

7g - 70h + 28

This expression is equivalent to the original 7(g - 10h + 4). It's now in a more straightforward form, easier to understand and use in further calculations.

Practical Applications

This type of simplification is crucial in various fields, including:

• Algebra: Solving equations and simplifying complex expressions.
• Geometry: Calculating areas and volumes of shapes.
• Physics: Formulating and solving equations related to motion, forces, and other physical phenomena.
• Computer Science: Developing algorithms and solving problems involving variables and calculations.

Conclusion

The seemingly complex expression 7(g - 10h + 4) becomes manageable once we understand and apply the distributive property of multiplication. By breaking down the expression and multiplying each term within the parentheses by 7, we arrive at the simplified and equivalent expression 7g - 70h + 28. This skill is foundational to many mathematical and scientific applications.