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RD Chapter 4 Algebraic Identities Ex MCQS Solutions

Question - 21 : -

Answer - 21 : -


Question - 22 : -
If a + b + c = 9 and ab + bc + ca = 23, then a3 + b3 + c3 – 3 abc =
(a) 108
(b) 207
(c) 669
(d) 729

Answer - 22 : -

a3 + b3 + c3 –3abc
= (a + b + c) [a2 + b2 + c2 –(ab + bc + ca)
Now, a + b + c = 9
Squaring,
a2 + b2 + c2 + 2 (ab + be + ca)= 81
⇒ a2 + b2 + c2 + 2 x 23 = 81
⇒ a2 + b2 + c2 + 46 = 81
⇒ a2 + b2 + c2 = 81 – 46 = 35
Now, a3 + b3 + c3 – 3 abc = (a+ b + c) [(a2 + b2 + c2) – (ab + bc+ ca)
= 9[35 -23] = 9 x 12=108                    (a)

Question - 23 : -

Answer - 23 : -


Question - 24 : - The product (a + b) (a – b) (a2 – ab +b2) (a2 + ab + b2) is equal to
(a) a6 +   b6
(b) a6 – b6
(c) a3 – b3
(d) a3 + b3

Answer - 24 : -

(a + b) (a – b) (a2 – ab + b2) (a2 +ab +b2)
= (a + b) (a2-ab + b2) (a-b) (a2 + ab + b2)
= (a3 + b3) (a3 – b3)
= (a3)2 – (b3)2 = a6 –b6   (b)

Question - 25 : - The product (x2 – 1) (x4 +x2 + 1) is equal to
(a) x8 –   1
(b) x8 + 1
(c) x6 –   1
(d) x6 + 1

Answer - 25 : -

(x2 – 1) (x4 + x2 +1)
= (x2)3 – (1)3 = x6 –1                           (c)

Question - 26 : -

Answer - 26 : -


Question - 27 : -

Answer - 27 : -


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