Using the properties of determinants in evaluate:
= (x2 – x + 1) × (x + 1) – (x + 1) × (x – 1)
= x (x2 – x + 1) + 1 (x2 – x + 1) – (x2 – 1)
[∵ (a – b)(a + b) = (a2 – b2)]
= x3 – x2 + x + x2 – x + 1 – x2 + 1
= x3 – x2 + 2
1
Using the properties of determinants in evaluate:
= (x2 – x + 1) × (x + 1) – (x + 1) × (x – 1)
= x (x2 – x + 1) + 1 (x2 – x + 1) – (x2 – 1)
[∵ (a – b)(a + b) = (a2 – b2)]
= x3 – x2 + x + x2 – x + 1 – x2 + 1
= x3 – x2 + 2