Question

QUESTION 4 Factorise fully by using the appropriate grouping: 4.1) \( 4 a-8 b-a x^{2}+2 b x^{2} \) 4.2) \( 3 x^{3}-3 y^{3}-a x+a y \) 4.3) \( 4 x^{2}-25 p^{2}-4 x+1 \)

Ask by Allan Hall. in South Africa
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

1. **4.1) \( 4a - 8b - ax^2 + 2bx^2 \):** \[ (a - 2b)(2 - x)(2 + x) \] 2. **4.2) \( 3x^3 - 3y^3 - ax + ay \):** \[ (x - y)\Bigl[3(x^2 + xy + y^2) - a\Bigr] \] 3. **4.3) \( 4x^2 - 25p^2 - 4x + 1 \):** \[ (2x - 1 - 5p)(2x - 1 + 5p) \]

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To tackle these factorization problems by grouping, let’s break down each one into manageable parts. 1. **4.1)** \( 4a - 8b - ax^2 + 2bx^2 \) can be grouped as \( (4a - 8b) + (-ax^2 + 2bx^2) \). From the first group, you can factor out \( 4 \) to get \( 4(a - 2b) \), and from the second group, factor out \( -x^2 \) which gives \( -x^2(a - 2b) \). So, combined you have \( (4 - x^2)(a - 2b) \). 2. **4.2)** \( 3x^3 - 3y^3 - ax + ay \) can be rearranged into \( (3x^3 - 3y^3) + (-ax + ay) \). Factors from the first term lead to \( 3(x^3 - y^3) \) which can then be further factored to \( 3(x - y)(x^2 + xy + y^2) \). The second group gives you \( -a(x - y) \). Overall, you can factor out \( (x - y) \) to result in \( (x - y)(3(x^2 + xy + y^2) - a) \). 3. **4.3)** \( 4x^2 - 25p^2 - 4x + 1 \) can be rearranged as \( (4x^2 - 4x) + (-25p^2 + 1) \). The first grouping allows you to factor out \( 4 \) leading to \( 4(x^2 - x) \), and the second can be recognized as a difference of squares, resulting in \( (5p - 1)(5p + 1) \). Thus we can further simplify to \( 4(x - \frac{1}{2})^2 - (5p - 1)(5p + 1) \) or expressed differently depending on the context required. Feel free to let me know if you need assistance with any further steps or explanations!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy