## 36x – 8y2 when x = 3 and y = –6 what is the value?

*When x = 3 and y = -6, the value of the expression 36x – 8y^2 is -720. This result is obtained by substituting the given values into the expression and performing the necessary calculations: 36(3) – 8(-6)^2 = 108 – 288 = -720.*

**Evaluating the Expression 36x – 8y^2: Understanding Substitution and Mathematical Evaluation**

In the realm of algebra, expressions like 36x – 8y^2 are a fundamental component of mathematical equations and problem-solving. They allow us to represent relationships and perform calculations. In this comprehensive blog post, we will explore the process of evaluating the expression 36x – 8y^2 when x = 3 and y = -6, shedding light on the significance and applications of such evaluations.

**Understanding Algebraic Expressions:**

An algebraic expression is a mathematical phrase that contains variables, constants, and operations. In this expression, 36x – 8y^2:

- “x” and “y” are variables.
- “36” and “8” are constants.
- “-” represents subtraction.

**Step 1: Substituting Values for Variables:**

To evaluate the expression 36x – 8y^2 when x = 3 and y = -6, we start by substituting these values into the expression:

36x – 8y^2 = 36(3) – 8(-6)^2

**Step 2: Performing Arithmetic Operations:**

Now, let’s simplify the expression by performing the necessary arithmetic operations:

36(3) – 8(-6)^2 = 108 – 8(36)

**Step 3: Continue Simplifying:**

Further simplifying:

108 – 8(36) = 108 – 288

**Step 4: Final Calculation:**

Finally, perform the subtraction:

108 – 288 = -180

**Conclusion:**

The value of the expression 36x – 8y^2 when x = 3 and y = -6 is -180.

**Significance of Expression Evaluation:**

Evaluating algebraic expressions is a fundamental skill in mathematics with real-world applications:

**Physics:**Scientists and engineers use expressions to model physical phenomena, making calculations to understand and predict the behavior of objects and systems.**Finance:**Financial analysts use expressions to evaluate investments, assess risk, and calculate returns.**Engineering:**Engineers employ expressions to design and analyze structures, systems, and circuits.**Statistics:**Statisticians use expressions to process data, calculate probabilities, and perform statistical analyses.**Computer Science:**Programmers write code that involves evaluating expressions to perform tasks in software and algorithms.

**In-Depth Exploration:**

To delve deeper into this topic, we can explore more complex algebraic expressions, discuss the order of operations (PEMDAS/BODMAS), and provide examples from various fields where expression evaluation is crucial.

**Conclusion:**

Evaluating algebraic expressions, as demonstrated with 36x – 8y^2, is an essential mathematical skill with applications in diverse fields. The ability to substitute values into expressions and perform calculations is fundamental for problem-solving and mathematical understanding, making it a valuable tool in both academic and practical contexts.

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