Factorize completely 9y2 - 16X2

Analysis

The expression given is $9y^2 - 16x^2$. This is a classic algebraic expression that fits the Difference of Two Squares pattern.

Concept: Difference of Two Squares

In algebra, the difference of two squares follows the identity:

To solve this, we need to express both terms in the given expression as perfect squares.

Step-by-Step Solution

1. Identify the squares: • The first term is $9y^2$. Since $9 = 3^2$, we can write this as $(3y)^2$. • The second term is $16x^2$. Since $16 = 4^2$, we can write this as $(4x)^2$.

2. Rewrite the expression: Substituting these back into the original expression, we get: $$(3y)^2 - (4x)^2$$

3. Apply the identity: Using the formula $a^2 - b^2 = (a - b)(a + b)$, where $a = 3y$ and $b = 4x$: $$(3y - 4x)(3y + 4x)$$

Conclusion

Comparing our result $(3y - 4x)(3y + 4x)$ with the given options, it matches option D.

Exam Tip

Whenever you see a binomial (two terms) with a minus sign between them, always check if both terms are perfect squares (like 1, 4, 9, 16, 25, 36, etc.). If they are, you can immediately use the $(a-b)(a+b)$ shortcut to save time during your JAMB exam!