Question

2. Factorise:
(1) X^7 – 64x​

Answer 1

Step-by-step explanation:

..........................

Answer 2

Answer: x(x³ +8)(x³ - 8) or, x{(x² - 4)(x⁴ + 16 +4x²)}

Step-by-step explanation:

Given,

x⁷ - 64x

Taking 'x' as common,

= x(x⁶ - 64)

Writing 64 as 2⁶,

= x(x⁶ - 2⁶) .............i)

= x{(x³)² - (2³)²}

= x{(x³ + 2³)(x³ - 2³)}

= x(x³ + 2³)(x³ - 2³)

= x(x³ +8)(x³ - 8)

Again from equation i),

=  x(x⁶ - 2⁶)

= x{(x²)³ - (2²)³}

= x{(x² - 2²)(x⁴ + 2⁴ + x²2²)}

= x{(x² - 4)(x⁴ + 16 +4x²)}

Note:- In the first answer formula used to expland is:-

(a² - b²) = (a - b)(a + b)

While in the second answer,

(a³ - b³) = (a - b)(a² + b² +ab)