15 Aug, 2024
· Mathematics

What is the value of the expression when n = 3 ?

-2n (5 + n - 8 - 3n)

Short Answer
Some answer Some answer Some answer
Long Explanation

Explanation

To find the value of the expression when n=3n = 3, we'll first simplify the given expression:

−2n(5+n−8−3n)-2n (5 + n - 8 - 3n)

Simplify the expression inside the parentheses

Combine like terms inside the parentheses:

5+n−8−3n=5−8+n−3n=−3−2n5 + n - 8 - 3n = 5 - 8 + n - 3n = -3 - 2n

Now, we substitute this back into the original expression:

−2n⋅(−3−2n)-2n \cdot (-3 - 2n)

Substitute n=3n = 3

Next, we substitute n=3n = 3 into the simplified expression:

−2(3)⋅(−3−2(3))-2(3) \cdot (-3 - 2(3))

This becomes:

−6⋅(−3−6)-6 \cdot (-3 - 6)

Further simplifying inside the parentheses:

−6⋅(−9)-6 \cdot (-9)

Final Calculation

Calculate the product:

−6⋅(−9)=54-6 \cdot (-9) = 54

Therefore, the value of the expression when n=3n = 3 is:

54\boxed{54}
Verified By
ER
Emily Rosen

Mathematics Content Writer at Math AI

Emily Rosen is a recent graduate with a Master's in Mathematics from the University of Otago. She has been tutoring math students and working as a part-time contract writer for the past three years. She is passionate about helping students overcome their fear of math through easily digestible content.

mathematics
Concept

To Answer This Question

Understanding the Concept

To address this concept comprehensively, it is important to identify the key elements required:

Gathering Necessary Information

  1. Identify the Problem: First, comprehend the question's context. What is it really asking? This step involves breaking down the question into understandable parts.

  2. Relevant Data and Theories: Compile all necessary data and relevant theories. This may include:

  • Scientific principles
  • Mathematical formulas
  • Historical facts
  • Literature references
  1. Critical Analysis: Analyze the data thoroughly to form a coherent and accurate response. Apply critical thinking to establish connections between different pieces of information.

Mathematical Representation

If the question involves mathematical computations or theoretical physics, represent your final answer as clearly as possible. For example:

If x2+y2=1, the possibility of dy can be found usingdy=−2x pm4x2−4(1−x2)2\text{If } x^2 + y^2 = 1, \text{ the possibility of } dy \text{ can be found using} \\ dy = \frac{-2x \ pm \sqrt{4x^2 - 4(1 - x^2)}}{2}

Bringing It All Together

Ensure that your answer is organized, clear, and directly addresses every aspect of the question. The synthesis of collected data, theoretical knowledge, and analytical skills is essential for a comprehensive and accurate answer.

Concept

I Used The Following Concepts: Simplifying Algebraic Expressions

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves reducing complicated expressions into simpler and more manageable forms. This process makes it easier to solve equations or understand the relationships between variables.

Basic Steps

  1. Combine Like Terms Like terms are terms that have the same variables raised to the same power. For example, 3x3x and 5x5x are like terms and can be combined:

    3x+5x=8x3x + 5x = 8x

  2. Use the Distributive Property The distributive property allows you to simplify expressions involving parentheses. For example:

    a(b+c)=ab+aca(b + c) = ab + ac

    So for 3(x+2)3(x + 2), distribute the 3:

    3(x+2)=3x+63(x + 2) = 3x + 6

  3. Eliminate Parentheses Apply the distributive property to remove parentheses and combine like terms where possible.

  4. Rearrange Terms Sometimes, rearranging the terms can make it easier to see which terms can be combined. For example, in the expression 2+3x−x+42 + 3x - x + 4, rearrange to combine like terms:

    3x−x+2+4=2x+63x - x + 2 + 4 = 2x + 6

Example

Let's simplify the following algebraic expression:

2x+3(x−2)+42x + 3(x - 2) + 4

Start by using the distributive property on 3(x−2)3(x - 2):

2x+3x−6+42x + 3x - 6 + 4

Next, combine like terms:

(2x+3x)+(−6+4)(2x + 3x) + (-6 + 4)

Which simplifies to:

5x−25x - 2

Hence, the simplified form of the expression is:

5x−25x - 2

Key Points

  • Combine like terms to reduce the number of terms.
  • Distribute terms inside parentheses to simplify.
  • Rearrange terms logically to spot combinable terms.