Question

Find the continued product:

(i) (x +1)(x – 1)(x² + 1) 

(ii) (x- 3)(x + 3)(x² + 9) 

(iii) (3x – 2y)(3x + 2y)(9x² + 4y²) 

(iv) (2p + 3)(2p – 3)(4p² + 9)

Answer 1

(i) (x +1)(x – 1)(x² + 1) 

We know that, from formula, 

(a + b)(a – b) = a² – b² 

(x + 1)(x – 1) (x² + 1) = (x² – 1)(x² + 1) 

= (x²)² – 1 = x⁴ – 1

(ii) (x- 3)(x + 3)(x² + 9) 

We know that, from formula, 

(a + b)(a – b) = a² – b² 

(x – 3)(x + 3)(x² + 9) 

= (x² – 9)(x² + 9) 

= (x²)² – 9² = x⁴ – 81

(iii) (3x – 2y)(3x + 2y)(9x² + 4y²) 

We know that, from formula, 

(a + b)(a – b) = a² – b² 

(3x – 2y)(3x + 2y)(9x² + 4y²) 

= (9x² – 4y²)(9x² + 4y²) 

= 81x⁴ – 16y⁴

(iv) (2p + 3)(2p – 3)(4p² + 9) 

We know that, from formula, 

(a + b)(a – b) = a² – b² 

(2p + 3)(2p – 3)(4p² + 9) 

= (4p² – 9)(4p²+ 9) 

= (4p²)² – 9² = 16p⁴ – 81