Expand (x2+(3/x))4 :, :x :≠ :0

Question

Expand (x2+(3/x))4 :, :x :≠ :0 (A) x8+12x5+54x2+(108/x)+(81/x4) (B) x8-12x5+54x2-(108/x)-(81/x4) (C) x8-12x5-54x2+(108/x)+(81/x4) (D) None of these

Tardigrade Admin · Accepted Answer

We have ; (x2+(3/x))4 = 4C0(x2)4+ 4C1(x2)3((3/x))+ 4C2(x2)2((3/x))2 + 4C3(x2)((3/x))3+ 4C4((3/x))4 = x8+4x6⋅(3/x)+6x4⋅(9/x2)+4x2⋅(27/x3)+(81/x4) = x8+12x5+54x2+(108/x)+(81/x4).

Q. Expand $(x^{2} + \frac{3}{x})^{4}, x \neq = 0$

$x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}$

$x^{8} - 12 x^{5} + 54 x^{2} - \frac{108}{x} - \frac{81}{x ^{4}}$

$x^{8} - 12 x^{5} - 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}$

None of these

Q. Expand (x2+x3​)4,x=0

x8+12x5+54x2+x108​+x481​

x8−12x5+54x2−x108​−x481​

x8−12x5−54x2+x108​+x481​

None of these

We have ; (x2+x3​)4=4C0​(x2)4+4C1​(x2)3(x3​)+4C2​(x2)2(x3​)2 +4C3​(x2)(x3​)3+4C4​(x3​)4 =x8+4x6⋅x3​+6x4⋅x29​+4x2⋅x327​+x481​ =x8+12x5+54x2+x108​+x481​.

Q. Expand $(x^{2} + \frac{3}{x})^{4}, x \neq = 0$

$x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}$

$x^{8} - 12 x^{5} + 54 x^{2} - \frac{108}{x} - \frac{81}{x ^{4}}$

$x^{8} - 12 x^{5} - 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}$