1. Let's start by stating the problem: factoring algebraic expressions is rewriting them as a product of simpler expressions. 2. The most common methods include factoring out the greatest common factor (GCF), factoring trinomials, difference of squares, and factoring by grouping. 3. For example, to factor $6x^2 + 9x$, first find the GCF of 6 and 9, which is 3, and the variable part common to both terms, which is $x$. 4. Factor out the GCF: $$6x^2 + 9x = \cancel{3x} \left(\frac{6x^2}{\cancel{3x}} + \frac{9x}{\cancel{3x}}\right) = 3x(2x + 3)$$ 5. This means $6x^2 + 9x$ factors to $3x(2x + 3)$. 6. Remember, always look for the GCF first before trying other methods. 7. For trinomials like $x^2 + 5x + 6$, find two numbers that multiply to 6 and add to 5, which are 2 and 3. 8. So, $x^2 + 5x + 6 = (x + 2)(x + 3)$. 9. Practice these steps with different expressions to get comfortable with factoring. This is a fundamental skill in grade 10 math that helps simplify expressions and solve equations.