Factorize 16x 4 - y 4 - JAMB Mathematics 2023 Question

To factorize the given expression \(16x^4 - y^4\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\).

Let \(a = 2x^2\) and \(b = y^2\). Then, \(a^2 - b^2 = (2x^2 - y^2)(2x^2 + y^2)\).

Now, \(2x^2 - y^2\) is itself a difference of squares, where \(c = 2x\) and \(d = y\). Applying the difference of squares formula again, we get \(2x^2 - y^2 = (2x - y)(2x + y)\).

Substitute this back into the original expression:

\[16x^4 - y^4 = (2x - y)(2x + y)(2x^2 + y^2)\]

So, the correct factorization is:

\[16x^4 - y^4 = (2x - y)(2x + y)(2x^2 + y^2)\]