Question

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

Answer 1

Answer:

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

Step-by-step 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.

Answer 2

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

Step-by-step 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 $(2x-3)^5$

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

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

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