Problem 82 Simplify. $$4 x^{2}-(4 x)^{2}$... [FREE SOLUTION]

Chapter 9: Problem 82

Simplify. $$4 x^{2}-(4 x)^{2}$$

Short Answer

Expert verified

The simplified form of the given expression is $12x^{2}$

Step by step solution

Understand the Problem

First, make sure you understand what the problem is asking. In this case, it's asking to simplify the expression $4x^{2}-(4x)^{2}$. This involves rearranging and manipulating the terms using the rules of algebra.

Apply Rules of Exponents and Order of Operations

The term $4x^{2}$ is the square of $4x$, which means it's $4x * 4x = 16x^{2}$, and the term $4x^{2}$ can be left as is.

Perform Subtraction

Now, subtract the two terms. So we get $16x^{2} - 4x^{2} = 12x^{2}$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponents

Understanding exponents is key when simplifying algebraic expressions, especially when you encounter terms like $ (4x)^{2} $. An exponent indicates how many times a number, or base, is multiplied by itself. In $ (4x)^{2} $, the base $ 4x $ must be multiplied by itself.
To calculate this:

First, break it down: $ 4x \times 4x $.
Multiply the coefficients: $ 4 \times 4 = 16 $.
Then multiply the variables: $ x \times x = x^2 $.

Thus, $ (4x)^{2} = 16x^{2} $. Recognizing and correctly solving exponents helps reduce errors and simplifies your work.

Order of Operations

Order of operations dictates the sequence in which you perform calculations in a math problem. It's crucial if you're simplifying expressions to get consistent results.
For most calculations, follow this basic order using the acronym PEMDAS:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

In our example, $ 4x^{2} - (4x)^{2} $, handle the exponent first before moving to subtraction. This ensures calculations are accurate and align with mathematical standards.

Subtraction in Algebra

Subtraction is straightforward with numbers, but when combined with variables and coefficients, it demands careful attention. In algebra, each term's coefficient and corresponding variable powers must be accurately aligned to subtract.
Consider $ 16x^{2} - 4x^{2} $:

Both terms have the same variable part $ x^{2} $.
Only the coefficients (16 and 4) need to be subtracted: $ 16 - 4 = 12 $.
So, the result is $ 12x^{2} $.

Ensure the terms you're subtracting are 'like terms', meaning they have the same variable raised to the same power. This keeps the process smooth and correctly simplifies the expression.

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91影视

Simplify. $$4 x^{2}-(4 x)^{2}$$

Short Answer

Step by step solution

Understand the Problem

Apply Rules of Exponents and Order of Operations

Perform Subtraction

Key Concepts

Exponents

Order of Operations

Subtraction in Algebra

One App. One Place for Learning.

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