https://file.aiquickdraw.com/mathbot/file/1726913859346xpn8ob6b.jpg

Let's work through the first few questions from the image step by step. I'll start by addressing the factorization problems under section 1. Let me begin with:

### 1. Factorise

**(a) \( 6x^4y^3 - 10x^3y^4 \)**

We can factor out the greatest common factor (GCF) from both terms:

- The GCF of \(6x^4y^3\) and \(10x^3y^4\) is \(2x^3y^3\).

Thus, factorizing the expression:

\[
6x^4y^3 - 10x^3y^4 = 2x^3y^3(3x - 5y)
\]

---

**(b) \( 21a^3b^5 + 35a^5b^2 \)**

Similarly, we find the GCF of both terms:

- The GCF of \(21a^3b^5\) and \(35a^5b^2\) is \(7a^3b^2\).

So, we can factorize as:

\[
21a^3b^5 + 35a^5b^2 = 7a^3b^2(3b^3 + 5a^2)
\]

---

**(c) \( 25x^2y^2 - 10x^3y^2 + 15x^2y^3 \)**

We again extract the GCF from all terms. The GCF is \(5x^2y^2\), so we get:

\[
25x^2y^2 - 10x^3y^2 + 15x^2y^3 = 5x^2y^2(5 - 2x + 3y)
\]

Would you like to continue with the next set of problems, or would you prefer any specific details or clarifications?

### 5 Related Questions:
1. What is the importance of factoring expressions in solving equations?
2. How do we find the greatest common factor (GCF) in polynomials?
3. Can all quadratic expressions be factored? Why or why not?
4. What techniques are useful for factoring trinomials with leading coefficients?
5. How does factoring help simplify algebraic fractions?

### Tip:
Always check for the greatest common factor (GCF) before attempting more advanced factoring techniques. This simplifies the process significantly.

Factorise the algebraic expressions provided in the image for practice. Examples include 6x^4y^3 - 10x^3y^4, x^2 + 7x + 12, 36x^2 - 49y^2, and simplifying algebraic fractions like 2x^2 + 4x / (x^2 - x).

Practice factorising various algebraic expressions, including polynomials and quadratic equations. Learn how to factorize using the GCF, difference of squares, and simplify algebraic fractions. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation