I am Raushan Kumar. I am from India. I got AIR 51 in IMU CET and 97.45 percentile in mathematics in IIT JEE MAINS . I am very interested to share my maths knowledge .
In Exercises 19 - 40, use the Binomial Theorem to expand and simplify the expression.
$ \left(4x - 1\right)^3 - 2\left(4x - 1\right)^4 $
In Exercises 61 - 66, use the Binomial Theorem to expand and simplify the expression.
$ \left(3\sqrt{t} + \sqrt[4]{t}\right)^4 $
In Exercises 67 - 72, expand the expression in the difference quotient and simplify.
$ \dfrac{f\left(x + h\right) - f\left(x\right)}{h} \quad \quad $ Difference quotient
$ f(x) = \sqrt{x} $
$ f(x) = \dfrac{1}{x} $
In Exercises 101-104, prove the property for all integers $ r $ and $ n $ where $ 0 \le r \le n $.
$ _nC_r = _nC_{n - r} $
$ _nC_0 - _nC_1 + _nC_2 - \cdots \pm _nC_n = 0 $