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.