Let's factorize the expression:  
\[
a^2 + 6b^2 + 5ab - a - 2b
\]

1. Group the terms:
\[
(a^2 + 5ab - a) + (6b^2 - 2b)
\]

2. Factor each group:
- From the first group \(a^2 + 5ab - a\), factor out \(a\):
  \[
  a(a + 5b - 1)
  \]

- From the second group \(6b^2 - 2b\), factor out \(2b\):
  \[
  2b(3b - 1)
  \]

Now the expression is:
\[
a(a + 5b - 1) + 2b(3b - 1)
\]

There are no common factors between the terms, and this is the fully factorized form.

If you have any questions, or if you'd like further clarification, feel free to ask!

---

Here are 5 follow-up questions to explore:

1. Can you factorize a simpler quadratic expression like \(x^2 + 5x + 6\)?
2. How would you check if an expression is factorable or not?
3. What is the difference between grouping and using the quadratic formula for solving polynomials?
4. How would you factorize a perfect square trinomial?
5. What methods can you use to simplify polynomial expressions?

**Tip:** Always try to factor out common terms before applying other methods like grouping or the quadratic formula!

Learn how to factorize the polynomial a² + 6b² + 5ab - a - 2b using grouping terms. This step-by-step solution covers algebraic techniques like factoring out common terms and grouping. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation