Factorise the following: (i) x^2 + 4x + 4 (ii) 3a^2 – 24ab + 48b^2 (iii) x^5 – 16x (iv) m^2 + 1/m^2 – 23 (v) 6 – 216x^2

Question

Factorise the following: 

(i) x² + 4x + 4 

(ii) 3a² – 24ab + 48b² 

(iii) x⁵ – 16x 

(iv) m² + \(\frac{1}{m^2}\) – 23 

(v) 6 – 216x²

(vi) \(a^2+\frac{1}{a^2}-18\)

Answer 1

(i) x² + 4x + 4 

= (x + 2) (x + 2) = (x + 2)² 

∵ (a + b)² = a² + 2ab + b²

(ii) 3a² – 24ab + 48b² = 3[a² – 8ab + 16 b²] 

= 3 [a – 4b]² (∵ (a – b)² = a² – 2ab + b²)

(iii) x⁵ – 16x = x[x⁴ – 16] = x [(x²)² – 4²] 

= x (x² + 4) (x² – 4)= x (x² + 4) (x + 2) (x – 2)

(iv) m² + \(\frac{1}{m^2}\) – 23 

(v) 6 – 216x² = 6(1 - (6x)²) = 6(1 + 6x)(1 - 6x)

(vi) \(a^2+\frac{1}{a^2}-18\)