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RD Chapter 4- Algebraic Identities Ex-4.4 Interview Questions Answers

Question 1 : Find the following products:
(i) (3x + 2y) (9X2 – 6xy + Ay2)
(ii) (4x – 5y) (16x2 + 20xy + 25y2)
(iii) (7p4 + q) (49p8 – 7p4q + q2)

Answer 1 :


Question 2 : If x = 3 and y = -1, find the values of each of the following using in identity:

Answer 2 :


Question 3 : If a + b = 10 and ab = 16, find the value of a2 – ab + b2 and a2 + ab + b2.

Answer 3 :

a + b = 10, ab = 16 Squaring,
(a + b)2 = (10)2
a2 +b2 + lab = 100
a2 +b2 + 2 x 16 = 100
 a2 + b2 + 32 = 100
a2 +b2 = 100 – 32 = 68
Now, a2 – ab + b2 = a2 + b2 –ab = 68 – 16 = 52
and a2 + ab + b2 = a2 + b2 +ab = 68 + 16 = 84

Question 4 : If a + b = 8 and ab = 6, find the value of a3 + b3.

Answer 4 :

a + b = 8, ab = 6
Cubing both sides,
(a + b)3 = (8)3
a3 +b3 + 3 ab{a + b) = 512
 a3 + b3 + 3 x 6 x 8 = 512
 a3 + b3 + 144 = 512
 a3 + b3 = 512 – 144 = 368
a3 +b3 = 368

Question 5 : If a – b = 6 and ab = 20, find the value of a3-b3.

Answer 5 :

a – b = 6, ab = 20
Cubing both sides,
(a – b)3 = (6)3
 a3 – b3 – 3ab(a – b) = 216
 a3 – b3 – 3 x 20 x 6 = 216
 a3 – b3 – 360 = 216
 a3 -b3 = 216 + 360 = 576
a3 –b3 = 576

Question 6 : If x = -2 and y = 1, by using an identity find the value of the following: