Factorize 4a$^2$ - 9b$^2$

Analysis

The expression given is $4a^2 - 9b^2$. This is a classic algebraic expression that fits the Difference of Two Squares pattern.

Concept: Difference of Two Squares

The difference of two squares is a special algebraic identity that states:

To use this, you must be able to express both terms in the given problem as perfect squares.

Step-by-Step Solution

1. Identify the squares: • The first term is $4a^2$. Since $4 = 2^2$, we can write this as $(2a)^2$. • The second term is $9b^2$. Since $9 = 3^2$, we can write this as $(3b)^2$.

2. Rewrite the expression: Substitute these back into the original expression: $$(2a)^2 - (3b)^2$$

3. Apply the identity: Using the formula $x^2 - y^2 = (x - y)(x + y)$, where $x = 2a$ and $y = 3b$: $$(2a)^2 - (3b)^2 = (2a - 3b)(2a + 3b)$$

Conclusion

Comparing our result $(2a - 3b)(2a + 3b)$ with the given options, it matches option A perfectly.

Exam Tip

Whenever you see a binomial (two terms) with a minus sign in the middle, always check if both terms are perfect squares (like 1, 4, 9, 16, 25, $a^2$, $x^4$, etc.). If they are, you can immediately apply the $(x-y)(x+y)$ rule to save time during your JAMB exam!