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RD Chapter 5- Factorisation of Algebraic Expressions Ex-VSAQS Interview Questions Answers

Question 1 : If a + b + c = 0, then write the value of a3 + b2 + c2.

Answer 1 :

a + b+ c =0,                                                      ‘
Then a3 + b2 + c3 = 3 abc

Question 2 : If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.

Answer 2 :

a2 +b2 + c2 = 20, a + b + c = 0
(a + b+ c)2 = 0
a2 + b2 + c2 + 2(ab + bc + ca)= 0
 20 + 2(ab + be + ca) = 0
 2(ab + bc + ca) = -20
ab + bc + ca = 
202 =-10

Question 3 : If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 + c2.

Answer 3 :

a + b + c = 9, ab + bc + ca = 40
Squaring both sides,
(a + b + c)2 = (9)2
a2 + b2 + c2 + 2{ab + bc+ ca)  = 81
a2 +b2 + c2 + 2 x 40 = 81
 a2 + b2 + c2 + 80 = 81
a2 + b2 + c2 = 81 – 80 = 1

Question 4 : If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.

Answer 4 :

a2 + b2 + c2 = 250, ab + bc +ca = 3
(a+ b + c)2 = a2 + b2 + c2 +2(ab + bc +ca)
= 250+ 2 x3 =250 + 6 = 256
=(±16)2
b c = ±16

Question 5 : Write the value of 253 – 753 + 503.

Answer 5 :

253 – 753 + 503
Let a = 25, b = -75 and c = 50
 a + b + c = 25 – 75 + 50 = 0
a3 +b2 + c3 = 3abc
 253 + (-75)3 + 503
= 3 x 25 x (-75)- x 50 = -281250

Question 6 : Write the value of 483 – 303 – 183.

Answer 6 :

483 – 303 – 183
Let a = 48, b = -30, c = -18
a + b+ c = 48 – 30 – 18 = 0
 a2 + b2 + c2 = 3abc
 483 – 303 – 183
= 3 x 48 x (-30) (-18)
= 77760

Question 7 :

Answer 7 :


Question 8 : Write the value of 303 + 203 – 503.

Answer 8 :

303 + 203 – 503
Let a = 30, b – 20, c = -50
 a + b + c = 30 + 20 -50 = 50 – 50 = 0
a3 +b3 + c3 = 3 abc
 303 + 203 – 503 = 3 x 30 x 20 x(-50)
= 90000

Question 9 : Factorize: x4 + x2 + 25.

Answer 9 :

x4 + x2 + 25
 (x2)2 + (5)2 + 2x2 x5 – 2x2 x 5 +x2
 (x2)2 + (5)2 + 10x2 –10x2 + x2
= (x2)2 + (5)2 + 10x2 –9x2
= (x2 + 5)2 – (3x)2   {
a2-b2 =(a + b) (a – b)}
= (x2 + 5 – 3x) (x2 + 5 + 3x)
= (x2 – 3x + 5) (x2 + 3x + 5)

Question 10 : Factorize: x2 – 1 – 2a – a2.

Answer 10 :

x2 – 1 – 2 a – a2
= x2 – (1 +2a + a2) – (x)2 –(1 + a){
a2 –b2 = (a + b) (a – b)}
= (x + 1 + a) (x – 1 – a)
= (x + a + 1) (x – a – 1)


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RD Chapter 5- Factorisation of Algebraic Expressions Ex-VSAQS Contributors

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