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)
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
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