Expand x 3-2- x 26 using binomial expansion-

Using the binomial expansion, we get (x^3 2/x^2 )^6 = ^6C_0 (x^3)^6 ^6C_1 ((x^3)^5) (2/x^2 ) +^6C_2 ((x^3)^4) (2/x^2 )^2 ^6C_3 (x^3)^3 (2/x^2 )^3 +^6C_4(x ...

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Byju's Answer

Standard XII

Mathematics

Binomial Expression

Expand x 3-2/...

Question

Expand ${(x^{3} - \frac{2}{x^{2}})}^{6}$ using binomial expansion.

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Solution

Using the binomial expansion, we get
${(x^{3} - \frac{2}{x^{2}})}^{6} =^{6} C_{0} (x^{3})^{6} -^{6} C_{1} ((x^{3})^{5}) (\frac{2}{x^{2}}) +^{6} C_{2} ((x^{3})^{4}) {(\frac{2}{x^{2}})}^{2} -^{6} C_{3} (x^{3})^{3} {(\frac{2}{x^{2}})}^{3} +^{6} C_{4} (x^{3})^{2} {(\frac{2}{x^{2}})}^{4} -^{6} C_{5} x^{3} {(\frac{2}{x^{2}})}^{5} +^{6} C_{6} {(\frac{2}{x^{2}})}^{6} = x^{18} - 12 x^{13} + 60 x^{8} - 160 x^{3} + \frac{240}{x^{2}} - \frac{192}{x^{7}} + \frac{64}{x^{12}}$

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Expand (x3−2x2)6 using binomial expansion.

Using the binomial expansion, we get (x3−2x2)6=6C0(x3)6−6C1((x3)5)(2x2)+6C2((x3)4)(2x2)2−6C3(x3)3(2x2)3+6C4(x3)2(2x2)4−6C5x3(2x2)5+6C6(2x2)6=x18−12x13+60x8−160x3+240x2−192x7+64x12

Expand ${(x^{3} - \frac{2}{x^{2}})}^{6}$ using binomial expansion.