Question

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(i) (2x² - 3/x)³ 

(ii) (2x² - 3√(1 - x²))⁴ + (2x² + 3√(1 - x²))⁴

Answer 1

(i) (2x² - 3/x)³ 

(ii) Taking 2x² as a and 3√(1 - x²) as b we have (a - b)4 + (a - b)⁴

Now

Similarly (a + b)⁴ = a⁴ + 4a³ b + 6a² b² + 4ab³ + b⁴ 

∴ (a – b)⁴ + (a + b)⁴ = 2[a⁴ + 6a² b² + b⁴] 

Substituting the value of a and b we get

= 2[16x⁸ + 216x⁴ (1 – x²) + 81(1 – x²)²] 

= 2[16x⁸ + 216x⁴ – 216x⁶ + 81 + 81x⁴ – 162x²] 

= 2[16x⁸ – 216x⁶ + 297x⁴ – 162x² + 81] 

= 32x⁸ – 432x⁶ + 594x⁴ – 324x² + 162