Math, asked by ananda1970biswas, 10 months ago

(x+1)^6-(x-1)^6
Factorize

Answers

Answered by ᏕɱartYᎶᴜʀɭ

Step-by-step explanation:

(x + 1)⁶ - (x - 1)⁶

(x + 1)⁶ - (x - 1)⁶= (x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 ) - (x⁶ - 6x⁵ +15x⁴ -20x³ + 15x²-6x + 1)

(x + 1)⁶ - (x - 1)⁶= (x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 ) - (x⁶ - 6x⁵ +15x⁴ -20x³ + 15x²-6x + 1)= x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 - x⁶ + 6x⁵ - 15x⁴ +20x³ -15x² + 6x - 1

(x + 1)⁶ - (x - 1)⁶= (x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 ) - (x⁶ - 6x⁵ +15x⁴ -20x³ + 15x²-6x + 1)= x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 - x⁶ + 6x⁵ - 15x⁴ +20x³ -15x² + 6x - 1= 12x⁵ + 40x³ + 12x

(x + 1)⁶ - (x - 1)⁶= (x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 ) - (x⁶ - 6x⁵ +15x⁴ -20x³ + 15x²-6x + 1)= x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 - x⁶ + 6x⁵ - 15x⁴ +20x³ -15x² + 6x - 1= 12x⁵ + 40x³ + 12x= 4x (3x⁴ + 10x² + 3)

Answered by Anonymous

Answer :D

(x + 1)⁶ - (x - 1)⁶

= (x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 ) - (x⁶ - 6x⁵ +15x⁴ -20x³ + 15x²-6x + 1)

= x⁶ + 6x⁵ + 15x⁴ + 20x³ + 15x² + 6x + 1 - x⁶ + 6x⁵ - 15x⁴ +20x³ -15x² + 6x - 1

= 12x⁵ + 40x³ + 12x

= 4x (3x⁴ + 10x² + 3)

= 4x (x² + 3) (3x² + 1)

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