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**Algebraic Expressions and Identities **

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****(NCERT Ex 9.2 Answers)**

**(NCERT Ex 9.2 Answers)**

**Q1: Find the product of following pair of monomials.**

(i) 4 , 7p

(i) 4 , 7p

Answer:

4 ☓ 7p = 4 ☓ 7 ☓ p = 28p

**(ii) -4p , 7p**

Answer:

-4p ☓ 7p = -4 ☓ p ☓ 7 ☓ p = (-4☓7)☓ (p☓ p) = -28p

^{2}

**(iii) 4p , 7pq**

Answer:

-4p ☓ 7p = -4 ☓ p ☓7 ☓ p ☓ q = (-4☓ 7)☓ (p☓ p☓ q) = -28p

^{2}q

**(iv) 4p**

^{3}, -3pAnswer:

4p

^{3}☓ -3p = 4 ☓(-3) ☓ p ☓ p☓ p☓ p = -12p

^{4}

**(v) 4p , 0**

Answer:

4p ☓ 0 = 4☓ p☓ 0 = 0

**Q2: Find the areas of rectangles with the following pairs of monomials as their lengths**

and breadths respectively.

(p , q);(10m , 5n);(20x

and breadths respectively.

(p , q);(10m , 5n);(20x

^{2}, 5y^{2});(4x , 3x^{2});(3mn ,4np)Answer:

We know that,

Area of rectangle = Length ☓ Breadth

Area of 1

^{st}rectangle = p ☓ q = pq

Area of 2

^{nd}rectangle = 10m ☓ 5n = 10☓ 5 ☓ m ☓ n = 50mn

Area of 3

^{rd}rectangle = 20x

^{2}☓ 5y

^{2}= 20☓ 5 ☓ x

^{2}☓ y

^{2}= 100x

^{2}y

^{2}

Area of 4

^{th}rectangle = 4x ☓ 3x

^{2}= 4☓3 ☓ x ☓ x

^{2}= 12x

^{3}

Area of 5

^{th}rectangle = 3mn ☓4np = 3☓ 4 ☓ m ☓ n ☓ n ☓ p = 12mn

^{2}p

**Q3: Complete the table of products.**

First Monomial (⇨) Second Monomial(⇩) |
2x | -5y | 3x^{2} |
-4xy | 7x^{2}y |
-9x^{2}y^{2} |

2x | 4x^{2} |
... | ... | ... | ... | ... |

-5y | ... | ... | -15x^{2}y |
... | ... | ... |

3x^{2} |
... | ... | ... | ... | ... | ... |

-4xy | ... | ... | ... | ... | ... | ... |

7x^{2}y |
... | ... | ... | ... | ... | ... |

-9x^{2}y^{2} |
... | ... | ... | ... | ... | ... |

Answer:

The table can be completed as follows.

First Monomial (⇨) Second Monomial(⇩) |
2x | -5y | 3x^{2} |
-4xy | 7x^{2}y |
-9x^{2}y^{2} |

2x | 4x^{2} |
-10xy | 6x^{3} |
-8x^{2}y |
14x^{3}y |
-18x^{3}y^{2} |

-5y | -10xy | 25y^{2} |
-15x^{2}y |
20xy^{2} |
-35x^{2}y^{2} |
45x^{2}y^{3} |

3x^{2} |
6x^{3} |
-15x^{2}y |
9x^{4} |
-12x^{3}y |
21x^{4}y |
-27x^{4}y^{2} |

-4xy | -8x^{2}y |
20xy^{2} |
-12x^{3}y |
16x^{2}y^{2} |
-28x^{3}y^{2} |
36x^{3}y^{3} |

7x^{2}y |
14x^{3}y |
-35x^{2}y^{2} |
21x^{4}y |
-28x^{3}y^{2} |
49x^{4}y^{2} |
-63x^{4}y^{3} |

-9x^{2}y^{2} |
-18x^{3}y^{2} |
45x^{2}y^{3} |
-27x^{4}y^{2} |
36x^{3}y^{3} |
-63x^{4}y^{3} |
81x^{4}y^{4} |

**Q4: Obtain the volume of rectangular boxes with the following length,breadth**

and height respectivly.

(i) 5a , 3a

(ii) 2p , 4q , 8r

(iii) xy , 2x

(iv) a , 2b , 3c

and height respectivly.

(i) 5a , 3a

^{2}, 7a^{4}(ii) 2p , 4q , 8r

(iii) xy , 2x

^{2}y , 2xy^{2}(iv) a , 2b , 3c

Answer:

We know that,

Volume = Length ☓ Breadth ☓ Height

(i) Volume= 5a ☓ 3a

^{2}☓ 7a

^{4}= 5☓ 3☓ 7☓a☓ a

^{2}☓a

^{4}= 105a

^{7}

(ii) Volume=2p☓ 4q ☓ 8r= 2☓ 4☓ 8☓ p☓ q☓ r = 64pqr

(iii) Volume=xy ☓ 2x

^{2}y☓ 2xy

^{2}= 2☓2☓ xy☓ x

^{2}y☓ xy

^{2}= 4x

^{4}y

^{4}

(iv) Volume= a ☓ 2b ☓ 3c= 2☓ 3☓ a☓ b☓ c = 6abc

**Q5: Obtain the product of**

(i) xy , yz , zx

(i) xy , yz , zx

Answer:

xy ☓ yz ☓ zx = x

^{2}y

^{2}z

^{2}

**(ii) a , -a**

^{2}, a^{3}Answer:

a☓ -a

^{2}☓ a

^{3}= -a

^{1 + 2 + 3}= -a

^{6}

**(iii) 2 , 4y , 8y**

^{2}, 16y^{3}Answer:

2☓ 4y☓ 8y

^{2}☓16y

^{3}= 2☓ 4☓ 8☓ 16☓y ☓y

^{2}☓y

^{3}= 1024y

^{6}

**(iv) a , 2b , 3c , 6abc**

Answer:

a☓ 2b☓ 3c☓ 6abc= 2☓ 3☓ 6☓ a☓ b ☓ c ☓ abc = 36a

^{2}b

^{2}c

^{2}

**(v) m , -mn , mnp**

Answer:

m ☓ (-mn)☓ mnp= -m

^{3}n

^{2}p

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