Find the continued product:(i) (x +1)(x – 1)(x2 + 1) (ii) (x- 3)(x

1.	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» (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

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»

(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