<ol class="abc-list"><li data-list-item-id="item-2a"><div class="list-item-paragraph">In the expansion of \(\left(x^2 - \frac{k}{x^2}\right)^8\), where&nbsp;\(k\) is a positive constant, the term independent of \(x\) is \(5670\).<br>Show that&nbsp;\(k = 3\).<span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-2b"><div class="list-item-paragraph">With this value of \(k\) in <strong>2(a)</strong>, find the coefficient of the \(x^4\) term in the expansion of \(\left(x^2 - \frac{k}{x^2}\right)^8 (2 + x^4)\).<span class="inline-marks">[4]</span></div></li></ol>

In the expansion of \(\left(x^2 - \frac{k}{x^2}\right)^8\), where \(k\) is a positive constant, the term independent of \(x\) is \(5670\).
Show that \(k = 3\).

With this value of \(k\) in **2(a)**, find the coefficient of the \(x^4\) term in the expansion of \(\left(x^2 - \frac{k}{x^2}\right)^8 (2 + x^4)\).

Binomial Theorem

Binomial Theorem