Question

Use binomial theorem to expand (2+X)5 in ascending powers of x up to the terms containing x3 and Use your expansion to find (1.9)5

Answer 1

Answer:

(2 + X)⁵ = 32 + 80X + 80X² + 40X³ + 10X⁴ + X⁵

Step-by-step explanation:

Use binomial theorem to expand (2+X)5

(2 + X)⁵

= ⁵C₅2⁵X⁰ + ⁵C₁2⁴X  + ⁵C₂2³X² + ⁵C₃2²X³ + ⁵C₄2¹X⁴ +  ⁵C₅2⁰X⁵

= 2⁵ + 5*2⁴X + 10*2³X² + 10*2²X³ + 5*2X⁴ + X⁵

= 32 + 80X + 80X² + 40X³ + 10X⁴ + X⁵

(2 + X)⁵ = 32 + 80X + 80X² + 40X³ + 10X⁴ + X⁵