## RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.1
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.2
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.4
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.5
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.6
- RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.7

**Find each of the following products (1-8)**

**Question 1.
**

**5x**

^{2}x 4x^{3 }**Solution:**

5x

^{2}x 4x

^{3}= 5 x 4 x x

^{2}x x

^{3}

= 20x

^{2 + 3}= 20x

^{s}

**Question 2.
**

**3a**

^{2}x 4b^{4 }**Solution:**

-3a

^{2}x 4b

^{4}= -3 x 4 x a

^{2}b

^{4 }= -12a

^{2}b

^{4}

**Question 3.
**

**(-5xy) x (-3x**

^{2}yz)**Solution:**

(-5xy) x (-3x

^{2}yz)

= (-5) x (-3)xy x x

^{2}yz

= 15x

^{1 + }

^{2}xy

^{1+ 1}z= 15x

^{3}y

^{2}z

**Question 4.**

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Find each of the following products : (9-17)**

**Question 9.
**

**(7ab) x (-5ab**

^{2}c) x (6abc^{2})**Solution:**

(7ab) x (-5ab

^{2}c) x (6abc

^{2})

= 7 x (-5) x 6 x a x a x a x b x b

^{2}x b x c x c

^{2 }=-210 x a

^{1+1+1 }x b

^{1+2+1}x c

^{1+2 }=-210 x a

^{3}b

^{4}c

^{3}

**Question 10.
**

**(-5a) x (-10a**

^{2}) x (-2a^{3})**Solution:**

(-5a) x (-10a

^{2}) x (-2a

^{3})

= (-5) (-10) (-2) x a x a

^{2}x a

^{3 }= -100a

^{1 + 2 + 3}= -100a

^{6}

**Question 11.
**

**(-4x**

^{2}) x (-6xy^{2}) x (-3yz^{2})**Solution:**

(-4x

^{2}) x (-6xy

^{2}) x (-3yz

^{2})

= (-4) x (-6) x (-3) x

^{2}x x x y

^{2}x y xz

^{2 }= -72x

^{2+1}x y

^{2+1}

*x*

_{z}

^{2}= 72x

^{3}y

^{3}z

^{3}

**Question 12.**

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.
**

**(2.3xy) x (0.1x) x (0.16)**

**Solution:**

(2.3xy) x (0.1x) x (0.16)

= 2.3 x 0.1 x 0.16 x x x x x y

= 0.0368x

^{1 +1}x y = 0.0368x

^{2}y

**Express each of the following products as a monomials and verify the result in each case for x = 1 : (18 -26)**

**Question 18.
**

**(3x) x (4x) x (-5x)**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.
**

**(5x**

^{4}) x (x^{2})^{3}x (2x)^{2 }**Solution:**

(5x

^{4}) x (x

^{2})

^{3}x (2x)

^{2}

= 5x

^{4}x x

^{2 x }

^{3}x 2x x 2x

= 5x

^{4}* x

^{6}x 4x

^{2}= 5 x 4 x x

^{4 + 6 + 2 }= 20x

^{12 }Verification:

L.H.S. = (5x

^{4}) x (x

^{2})

^{3}x (2x)

^{2}

^{ }= 5 x (1)

^{4}x [(1)

^{2}]

^{3}x (2 x 1)

^{2 }= 5 x 1 x (1)

^{2 x }

^{3}

_{x}(2)

^{2 }= 5 x 1

^{6}x 2

^{2}= 5 x 1 x 4 = 20

R.H.S. = 20x

^{12}= 20 (1)

^{12}= 20 x 1 = 20

∴ L.H.S. = R.H.S.

**Question 21.
**

**(x**

^{2})^{3}x (2x) x (-4x) x 5**Solution:**

(x

^{2})

^{3}x (2x) x (-4x) x (5)

= x

^{2 x}

^{3}X 2x X (-4x) X 5

= x

^{6}x 2x x (-4x) x 5 = 2 x (-4) x 5x

^{6}

^{+1 +1}

= -40x

^{8 }Verification

L.H.S. = (x

^{2})

^{3}x (2x) x (-4x) x (5)

= (1

^{2})

^{3}x (2 x 1) x (-4 x 1) x 5

= 1

^{2 x }

^{3 }x 2 x (- 4) x 5 = 1

^{6}x 2 x (-4) x 5

= 1 x 2 x (-4) x 5 = -40

R.H.S. = -40x

^{8}= -40 x (1)

^{8}

= -40 x 1 = -40

∴ L.H.S. = R.H.S.

**Question 22.
**

**Write down the product of -8x**

^{2}y^{6}and – 20xy Verify the product for x = 2.5, y = 1.**Solution:**

Product of -8x

^{2}y

^{6}and -20xy

= (-8x

^{2}y

^{6}) x (-20xy)

= -8 x (-20) x

^{2}x

_{x}x y

^{6}x y = 160x

^{2 + 1}x y

^{6 +}

^{ 1 }= 160x

^{3}y

^{3}

Verification.

L.H.S. = (-8x

^{2}y

^{6}) x (-20xy)

= -8 x (2.5)

^{2}x (1) x (-20 x 2.5 x 1)

= -8 x 6.25 x 1 x -20 x 2.5

= (-50) x (-50) = 2500

R.H.S. = 160 x = 160 (2.5)

^{3}x (1)

^{7 }= 160 x 15.625 x 1 =2500

∴ L.H.S. = R.H.S.

**Question 23.
**

**Evaluate : (3.2x**

^{6}y^{3}) x (2.1x^{2}y^{2}) when x = 1 and y = 0.5.**Solution:**

3.2x

^{6}y

^{3}x 2.1x

^{2}y

^{2 }= 3.2 x 2.1 x x

^{6+2 }x y

^{3+2}

= 6.72x

^{8}y

^{5}= 6.72 x (1)

^{8}x (0.5)

^{5 }= 6.72 x 1 x 0.03125

= 0.21

**Question 24.
**

**Find the value of (5x**

^{6}) x (-1.5x^{2}y^{3}) x (-12xy^{2}) when x = 1, y = 0.5.**Solution:**

**Question 25.
**

**Evaluate : (2.3a**

^{5}b^{2}) x (1.2a^{2}b^{2}) when a = 1, b = 0.5.**Solution:**

**Question 26.
**

**Evaluate : (-8x**

^{2}y^{6}) x (-20xy) for x = 2.5 and y = 1.**Solution:**

**Express each of the following products as a monomials and verify the result for x = 1,y = 2: (27-31)**

**Question 27.
**

**(-xy**

^{3}) x (yx^{3}) x (xy)**Solution:**

(-xy

^{3}) x (yx

^{3}) x (xy)

= -x x x

^{3 }x x x y

^{3 }x y x y = -x

^{1 }

^{+ }

^{3}

^{ + }

^{1}x y

^{3 + }

^{1}

^{ + }

^{1 }= -x

^{5}y

^{5 }Verification:

L.H.S. = (-xy

^{3}) x (yx

^{3}) x (xy)

= (-1 x 2

^{3}) x [2 x (1)

^{3}] x (1 X 2)

= (-1 x 8) x (2 x 1) x (1 x 2)

= -8 x 2 x 2 = -32

R.H.S. =-x

^{5}y

^{5}= -(1)

^{5}(2)

^{5 }= -1 x 32 =-32

∴ L.H.S. = R.H.S.

**Question 28.**

**Solution:**

**Question 29.**

**Solution:**

**Question 30.**

**Solution:**

**Question 31.**

**Solution:**

**Question 32.**

**Solution:**

**Question 33.**

**Solution:**

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