Question

Expand the following binomials expressions.

${(1-\frac{3x^2}{2})}^4$

Answer 1

${(1-\frac{3x^2}{2})}^4={}^4{C}_0{+}^4{C}_1(-\frac{3x^2}{2}){+}^4{C}_2{(-\frac{3x^2}{2})}^2{+}^4{C}_3{(-\frac{3x^2}{2})}^3{+}^4{C}_4{(-\frac{3x^2}{2})}^4$
$=1-6x^2+\frac{27}{2}{x}^4-\frac{27}{2}{x}^6+\frac{81}{16}{x}^8$.