{"id":17967,"date":"2026-05-02T20:17:47","date_gmt":"2026-05-02T14:17:47","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/binomial-coefficient-term-8\/"},"modified":"2026-05-02T20:17:47","modified_gmt":"2026-05-02T14:17:47","slug":"binomial-coefficient-term-8","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/binomial-coefficient-term-8\/","title":{"rendered":"Binomial Coefficient Term 8"},"content":{"rendered":"<p>In the expansion of (3x + -1y)^8, find the coefficient of x^5y^3.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>-13608<\/li>\n<li>56<\/li>\n<li>13608<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705,2720],"subject":[1425],"education_level":[1896],"class_list":["post-17967","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-binomial-theorem","subject-mathematics","education_level-hsc"],"mcq_note":"Use the binomial theorem and match the power of y to decide the value of k. Once k is known, the power of x is automatically n-k. The general term is C(8,k)(3x)^(8-k)(-y)^k. For k=3, the coefficient is C(8,3)\u00b73^5\u00b7-1^3=-13608. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.","mcq_options":[{"right":"yes","answer":"-13608"},{"right":"no","answer":"56"},{"right":"no","answer":"13608"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"},{"id":2720,"title":"Binomial Theorem","slug":"binomial-theorem"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/17967","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=17967"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17967"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17967"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17967"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}