15 (a) Factorise $a^2 - b^2$ (b) Hence, or otherwise, simplify fully $(x^2 + 4)^2 - (x^2 - 2)^2$ - Edexcel - GCSE Maths - Question 15 - 2018 - Paper 1

To simplify $(x^2 + 4)^2 - (x^2 - 2)^2$, we can again use the difference of squares formula.

Let:

• $A = x^2 + 4$
• $B = x^2 - 2$

Then we have:

$(x^2 + 4)^2 - (x^2 - 2)^2 = A^2 - B^2 = (A - B)(A + B)$

Now calculate $A - B$ and $A + B$:

1. Calculate $A - B$:

   $A - B = (x^2 + 4) - (x^2 - 2) = 4 + 2 = 6$

2. Calculate $A + B$:

   $A + B = (x^2 + 4) + (x^2 - 2) = 2x^2 + 2$

Putting it all together, we have:

$(x^2 + 4)^2 - (x^2 - 2)^2 = (6)(2x^2 + 2) = 12(x^2 + 1)$

Thus, the fully simplified expression is:

$12(x^2 + 1)$