## RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions VSAQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions VSAQS

**Other Exercises**

- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.1
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.2
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.3
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.4
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions VSAQS
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions MCQS

**Question 1.
**

**If a + b + c = 0, then write the value of a**

^{3 }+ b^{2}+ c^{2}.**Solution:**

∵ a + b + c = 0, ‘

Then a

^{3}+ b

^{2}+ c

^{3}= 3 abc

**Question 2.
**

**If a**

^{2}+ b^{2}+ c^{2}= 20 and a + b + c = 0, find ab + bc + ca.**Solution:**

a

^{2}+ b

^{2}+ c

^{2}= 20, a + b + c = 0

∴ (a + b + c)

^{2}= 0

a

^{2}+ b

^{2}+ c

^{2}+ 2(ab + bc + ca) = 0

⇒ 20 + 2(ab + be + ca) = 0

⇒ 2(ab + bc + ca) = -20

ab + bc + ca = \(\frac { -20 }{ 2 }\) = -10

**Question 3.
**

**If a + b + c = 9 and ab + bc + ca = 40, find a**

^{2}+ b^{2}+ c^{2}.**Solution:**

a + b + c = 9, ab + bc + ca = 40

Squaring both sides,

(a + b + c)

^{2}= (9)

^{2 }a

^{2}+ b

^{2}+ c

^{2}+ 2{ab + bc + ca) = 81

⇒ a

^{2}+ b

^{2}+ c

^{2}+ 2 x 40 = 81

⇒ a

^{2}+ b

^{2}+ c

^{2}+ 80 = 81

a

^{2}+ b

^{2}+ c

^{2}= 81 – 80 = 1

**Question 4.
**

**If a**

^{2}+ b^{2}+ c^{2}= 250 and ab + bc + ca = 3, find a + b + c.**Solution:**

a

^{2}+ b

^{2}+ c

^{2}= 250, ab + bc + ca = 3

(a + b + c)

^{2}= a

^{2}+ b

^{2}+ c

^{2}+ 2(ab + bc + ca)

= 250 + 2 x 3 = 250 + 6 = 256

= (±16)

^{2 }∴ a + b + c = ±16

**Question 5.
**

**Write the value of 25**

^{3}– 75^{3}+ 50^{3}.**Solution:**

25

^{3}– 75

^{3}+ 50

^{3 }Let a = 25, b = -75 and c = 50

∵ a + b + c = 25 – 75 + 50 = 0

∴ a

^{3}+ b

^{2}+ c

^{3}= 3abc

⇒ 25

^{3}+ (-75)

^{3}+ 50

^{3}

= 3 x 25 x (-75)- x 50 = -281250

**Question 6.
**

**Write the value of 48**

^{3}– 30^{3}– 18^{3}.**Solution:**

48

^{3}– 30

^{3}– 18

^{3 }Let a = 48, b = -30, c = -18

∵ a + b + c = 48 – 30 – 18 = 0

∴ a

^{2}+ b

^{2}+ c

^{2}= 3abc

⇒ 48

^{3}– 30

^{3}– 18

^{3}

= 3 x 48 x (-30) (-18)

= 77760

**Question 7.**

**Solution:**

**Question 8.
**

**Write the value of 30**

^{3}+ 20^{3}– 50^{3}.**Solution:**

30

^{3}+ 20

^{3}– 50

^{3 }Let a = 30, b – 20, c = -50

∵ a + b + c = 30 + 20 -50

^{=}50 – 50

^{=}0

∴ a

^{3}+ b

^{3}+ c

^{3}= 3 abc

⇒ 30

^{3}+ 20

^{3}– 50

^{3}= 3 x 30 x 20 x (-50)

= 90000

**Question 9.
**

**Factorize: x**

^{4}+ x^{2}+ 25.**Solution:**

x

^{4}+ x

^{2}+ 25

⇒ (x

^{2})

^{2}+ (5)

^{2}+ 2x

^{2}x 5 – 2x

^{2}x 5 +x

^{2}

⇒ (x

^{2})

^{2}+ (5)

^{2}+ 10x

^{2}– 10x

^{2}+ x

^{2 }= (x

^{2})

^{2}+ (5)

^{2}+ 10x

^{2}– 9x

^{2 }= (x

^{2}+ 5)

^{2}– (3x)

^{2 }{∵ a

^{2}-b

^{2}= (a + b) (a – b)}

= (x

^{2}+ 5 – 3x) (x

^{2}+ 5 + 3x)

= (x

^{2}– 3x + 5) (x

^{2}+ 3x + 5)

**Question 10.
**

**Factorize: x**

^{2}– 1 – 2a – a^{2}.**Solution:**

x

^{2}– 1 – 2 a – a

^{2 }= x

^{2}– (1 +2a + a

^{2}) – (x)

^{2}– (1 + a)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (x + 1 + a) (x – 1 – a)

= (x + a + 1) (x – a – 1)

Hope given RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions VSAQS are helpful to complete your math homework.

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