Question

x – 8x⁴ is equal to ______.

पर्याय

• (x – 2x²) (x + 4x²)

• (x + 2x²) (1 – 4x²)

• x(1 – 2x) (1 + 2x + 4x²)

• x(1 + 2x) (1 – 2x + 4x²)

Answer 1

x – 8x⁴ is equal to x(1 – 2x) (1 + 2x + 4x²).

Explanation:

We are asked to factorise:

x – 8x⁴

Step 1: Factor out the common term x:

x – 8x⁴ = x(1 – 8x³)

Step 2: Recognise 8x³ as a cube:

1 – 8x³ = 1³ – (2x)³

This is a difference of cubes:

a³ – b³ = (a – b) (a² + ab + b²), with a = 1 and b = 2x:

1 – (2x)³ = (1 – 2x) (1² + 1 · 2x + (2x)²)

= (1 – 2x) (1 + 2x + 4x²)

Step 3: Combine with the x we factored out:

x – 8x⁴ = x(1 – 2x) (1 + 2x + 4x²)