

Examples
Example 2 Important
Example 3 Important
Example 4
Example 5 Important Deleted for CBSE Board 2023 Exams
Example 6 Important Deleted for CBSE Board 2023 Exams
Example 7 Deleted for CBSE Board 2023 Exams
Example 8 Important Deleted for CBSE Board 2023 Exams
Example 9 Deleted for CBSE Board 2023 Exams
Example 10 Important Deleted for CBSE Board 2023 Exams
Example 11 Important Deleted for CBSE Board 2023 Exams
Example 12 Deleted for CBSE Board 2023 Exams
Example 13 Important Deleted for CBSE Board 2023 Exams
Example 14 Important Deleted for CBSE Board 2023 Exams
Example 15 Important Deleted for CBSE Board 2023 Exams
Example 16 Deleted for CBSE Board 2023 Exams
Example 17 Important Deleted for CBSE Board 2023 Exams
Last updated at Jan. 19, 2023 by Teachoo
Example 1 Expand ("x2 + " 3/x)^4 , x ≠ 0 We know that (a + b)n = nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + ….…. + nCn – 1 a1 bn – 1 + nCn bn Hence, (a + b)4 = 4C0 a4 + 4C1 a3 b1 + 4C2 a2 b2 + 4C3 a1b3 + 4C4 b4 = 4!/0!( 4 − 0)! a4 + 4!/(1! (4 − 1)!) a2 b2 + 4!/2!(4 − 2)! ab3 + 4!/(4!(4 − 4)!) b4 = 4!/(1 × 4!) a4 + 4!/(1 × 3!) a3 b + 4!/(2 × 2!) a2 b2 + 4!/(6 × 1!) ab3 + 4!/(4! × 0!) b4 = a4 + 4a3 b + 6a2 b2 + 4 ab3 + b4 Hence, (a + b)4 = a4 + 4a3 b + 6a2 b2 + 4 ab3 + b4 Putting a = x2 and b = 𝟑/𝒙 ("x2 + " 3/x)^4 = (𝑥^2 )^4 + 4 (𝑥^2 )^3 (3/x) + 6(𝑥^2 )^2 (3/x)^2 + 4 (𝑥^2 ) (3/x)^3+ (3/x)^4 = 𝑥8 + 4x6 . 3/𝑥 + 6𝑥4 . 9/𝑥2 + 4 𝑥2 . 27/𝑥3 + 81/𝑥4 = 𝑥8 + 12 𝑥6/𝑥 + 54 . 𝑥4/𝑥2 + 108 . 𝑥2/𝑥3 + 81/𝑥4 = 𝒙𝟖 + 12 𝒙5 + 54 𝒙2 + 𝟏𝟎𝟖/𝒙 + 𝟖𝟏/𝒙𝟒