We appreciate your visit to A cube is shrunk so that its side lengths of tex 2x tex are reduced by 3 units Using the Binomial Theorem which of the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's find the new volume of the cube using the Binomial Theorem.
1. Original Side Length: The original side length of the cube is [tex]\(2x\)[/tex].
2. New Side Length: The side length is reduced by 3 units, so the new side length is [tex]\(2x - 3\)[/tex].
3. Volume of a Cube Formula: The volume [tex]\(V\)[/tex] of a cube with side length [tex]\(s\)[/tex] is given by [tex]\(V = s^3\)[/tex].
4. Substitute New Side Length: We need to find [tex]\((2x - 3)^3\)[/tex].
5. Use the Binomial Theorem: The Binomial Theorem says that [tex]\((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\)[/tex].
- Here, [tex]\(a = 2x\)[/tex] and [tex]\(b = 3\)[/tex].
6. Calculate Each Term:
- First term: [tex]\(a^3 = (2x)^3 = 8x^3\)[/tex]
- Second term: [tex]\(-3a^2b = -3 \cdot (2x)^2 \cdot 3 = -3 \cdot 4x^2 \cdot 3 = -36x^2\)[/tex]
- Third term: [tex]\(3ab^2 = 3 \cdot (2x) \cdot 3^2 = 3 \cdot 2x \cdot 9 = 54x\)[/tex]
- Fourth term: [tex]\(-b^3 = -(3)^3 = -27\)[/tex]
7. Combine the Terms:
[tex]\((2x - 3)^3 = 8x^3 - 36x^2 + 54x - 27\)[/tex]
The correct expression for the new volume of the cube is:
[tex]\[8x^3 - 36x^2 + 54x - 27\][/tex]
So, the correct option is:
[tex]\(8x^3 - 36x^2 + 54x - 27\)[/tex]
1. Original Side Length: The original side length of the cube is [tex]\(2x\)[/tex].
2. New Side Length: The side length is reduced by 3 units, so the new side length is [tex]\(2x - 3\)[/tex].
3. Volume of a Cube Formula: The volume [tex]\(V\)[/tex] of a cube with side length [tex]\(s\)[/tex] is given by [tex]\(V = s^3\)[/tex].
4. Substitute New Side Length: We need to find [tex]\((2x - 3)^3\)[/tex].
5. Use the Binomial Theorem: The Binomial Theorem says that [tex]\((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\)[/tex].
- Here, [tex]\(a = 2x\)[/tex] and [tex]\(b = 3\)[/tex].
6. Calculate Each Term:
- First term: [tex]\(a^3 = (2x)^3 = 8x^3\)[/tex]
- Second term: [tex]\(-3a^2b = -3 \cdot (2x)^2 \cdot 3 = -3 \cdot 4x^2 \cdot 3 = -36x^2\)[/tex]
- Third term: [tex]\(3ab^2 = 3 \cdot (2x) \cdot 3^2 = 3 \cdot 2x \cdot 9 = 54x\)[/tex]
- Fourth term: [tex]\(-b^3 = -(3)^3 = -27\)[/tex]
7. Combine the Terms:
[tex]\((2x - 3)^3 = 8x^3 - 36x^2 + 54x - 27\)[/tex]
The correct expression for the new volume of the cube is:
[tex]\[8x^3 - 36x^2 + 54x - 27\][/tex]
So, the correct option is:
[tex]\(8x^3 - 36x^2 + 54x - 27\)[/tex]
Thanks for taking the time to read A cube is shrunk so that its side lengths of tex 2x tex are reduced by 3 units Using the Binomial Theorem which of the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
