Question

the coefficient of x^8 In (3x^2+5/x^3) is​

Answer 1

Heyyy,

Using Binomial Theorem,

(1 – 2x)5 = 5C0 + 5C1 (-2x) + 5C2 (-2x) + 5C3 (-2x) + 5C4 (-2x) + 5C5 (-2x)

= 1 + 5(-2x) + 10(-2x)2 + 10(-2x)3 + 5(-2x)4 + (-2x)5

= 1 + 5(-2x) + 10(4x2) + 10(-8x3) + 5(16x4) + (-32x5)

= 1 – 10x + 40x2 – 80x3 + 80x4 – 32x5.

2. Using Binomial Theorem,

3. Using Binomial Theorem,

(2x – 3)6 = 6C0(2x)6 + 6C1 (2x)5 (-3) + 6C2 (2x)4 (-3)2 + 6C3 (2x)3 (-3)3 + 6C4 (2x)2 (-3)4 + 6C5 (2x) (-3)5 + 6C6 (-3)6

= 64x6 + 6(32x5) (-3) + 15 (16x4) (9) + 20(8x3) (-27) + 15 (4x2) (81) + 6(2x) -(243) + 7

= 64x6 – 576x5 + 2160x4 – 4320x3 + 4860x2 – 2916x + 729