Question

What is the binomial expansion of (2x-3)^5

Answer 1

Answer:
`32x^5-240x^4+720x^3-1080x^2+810x-243`

Explanation:

Binomial expansion of
`(a+b)^n= ^nC_0 a^nb^0+^nC_1a^(n-1)b^1+^nC_2a^(n-2)b^2+....+^nC_na^0b^n`

In
`(2x-3)^5` , a= 2x and b= -3

Similarly, Binomial expansion of
`(2x-3)^5`

`= ^5C_0 (2x)^5(-3)^0+^5C_1(2x)^(4)(-3)^1+^5C_2(2x)^(3)(-3)^2+^5C_3(2x)^(2)(-3)^3+^5C_4(2x)^(1)(-3)^4+^5C_5(2x)^(0)(-3)^5\\\\=(1)(32x^5)+(5)(16x^4)(-3)+((5!)/(2!3!))(8x^3) (9)+((5!)/(2!3!))(4x^2) (-27)+(5)(2x)(81)+(1)(-243)\\\\=32x^5-240x^4+720x^3-1080x^2+810x-243`

Hence, Binomial expansion of
`(2x-3)^5`

`=32x^5-240x^4+720x^3-1080x^2+810x-243`

Answer 2

(2x - 3)⁵= 32x⁵ - 240x⁴ + 720x³ - 1080x² + 810x - 243

Explanation:

We need to write the expansion of Binomial (2x - 3)⁵

Here general form of binomial expansion is:

(a + b)ⁿ = ⁿC₀aⁿ + ⁿC₁aⁿ⁻¹b + ⁿC₂aⁿ⁻²b² + ⁿC₃aⁿ⁻³b³ + ... + ⁿCₙbⁿ

(2x - 3)⁵= ⁵C₀(2x)⁵ + ⁵C₁(2x)⁵⁻¹(-3) + ⁵C₂(2x)⁵⁻²(-3)² + ⁵C₃(2x)⁵⁻³(-3)³

+⁵C₄(2x)⁵⁻⁴(-3)⁴ + ⁵C₅(2x)⁵⁻⁵(-3)⁵

(2x - 3)⁵= (32x⁵) + 5(16x⁴)(-3) + 10(8x³)(-3)² + 10(4x²)(- 3)³ + 5(2x)(-3)⁴+(-3)⁵

(2x - 3)⁵= 32x⁵ - 240x⁴ + 720x³ - 1080x² + 810x - 243

That's the final answer.