8

(a) Find the first two non‑zero terms in the Maclaurin series of

(i) $\sin\bigl(x^{2}\bigr)$;
(ii) $\sin^{2}\bigl(x^{2}\bigr)$.

(b) Hence, or otherwise, find the first two non‑zero terms in the Maclaurin series of

$4x\,\sin\bigl(x^{2}\bigr)\cos\bigl(x^{2}\bigr).$