Factorise (4a + 3) $^2$ - (3a - 2)$^2$

Analysis

This problem requires the application of the Difference of Two Squares algebraic identity. The expression is in the form $x^2 - y^2$, where $x = (4a + 3)$ and $y = (3a - 2)$.

Concept

The difference of two squares formula is:

Using this identity allows us to factorise the expression without having to expand the squares and simplify a long polynomial, which saves time during your JAMB exam.

Solution

Given: $(4a + 3)^2 - (3a - 2)^2$

Step 1: Identify $x$ and $y$

• $x = (4a + 3)$
• $y = (3a - 2)$

Step 2: Apply the formula $(x - y)(x + y)$

• First bracket $(x - y)$: $(4a + 3) - (3a - 2)$ $= 4a + 3 - 3a + 2$ $= (4a - 3a) + (3 + 2)$ $= a + 5$

• Second bracket $(x + y)$: $(4a + 3) + (3a - 2)$ $= 4a + 3 + 3a - 2$ $= (4a + 3a) + (3 - 2)$ $= 7a + 1$

Step 3: Combine the results $(a + 5)(7a + 1)$

Conclusion

Comparing our result $(a + 5)(7a + 1)$ with the given options, it matches option C.

Exam Tip

Whenever you see a question in the format $A^2 - B^2$, always use the difference of two squares formula $(A-B)(A+B)$ instead of expanding the brackets. Expanding $(4a+3)^2$ and $(3a-2)^2$ separately is prone to sign errors (especially with the negative sign in the middle) and takes much longer to solve.