What is the coefficient of y2 in the expansion of $(\sqrt{2}y^2 - 5\sqrt{3})^3$ ?
Answer & explanation
Correct answer: option 3
We know that,
(a – b)3 = a3 – b3 – 3a2b + 3ab2
Given,
(\(\sqrt { 2}\)y2 – 5\(\sqrt { 3}\))3
= (\(\sqrt { 2}\) y2)3 – (5\(\sqrt { 3}\))3 – 3.( \(\sqrt { 2}\) y2)2.(5\(\sqrt { 3}\)) + 3.( \(\sqrt { 2}\) y2)(5\(\sqrt { 3}\))2
= 2\(\sqrt { 2}\) y6 – 375\(\sqrt { 3}\) 3 – 30\(\sqrt { 3}\) y4 + 225\(\sqrt { 2}\) y2
Coefficient of y2 = 225\(\sqrt { 2}\)