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Question -

(a) Simplify: 3x(4x тАУ 5) + 3 and find its values for (i) x = 3 (ii) x = 1/2.
(b) Simplify: a(a2 + a + 1) + 5 and find its value for (i) a = 0 (ii) a = 1 (iii) a = -1



Answer -

(a) We have 3x(4x тАУ 5) + 3 = 4x ├Ч 3x тАУ 5 ├Ч 3x + 3 = 12x2┬атАУ15x + 3
(i) For x = 3, we have
12 ├Ч (3)2┬атАУ15 ├Ч 3 + 3 = 12 ├Ч 9 тАУ 45 + 3 = 108 тАУ 42 = 66

(b) We have a(a2┬а+a + 1) + 5
= (a2┬а├Чa) + (a ├Ч a) + (1 ├Ч a) + 5
= a3┬а+a2┬а+a + 5
(i) For a = 0, we have
= (0)3┬а+(0)2┬а+(0) + 5 = 5
(ii) For a = 1, we have
= (1)3┬а+(1)2┬а+(1) + 5 = 1 + 1 + 1 + 5 = 8
(iii) For a = -1, we have
= (-1)3┬а+(-1)2┬а+(-1) + 5 = -1 + 1 тАУ 1 + 5 = 4

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