RBSE Solutions for Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.2 is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 10 गुणनखण्ड Exercise 10.2.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 10 |

Chapter Name |
गुणनखण्ड |

Exercise |
Exercise 10.2 |

Number of Questions |
3 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.2

प्रश्न 1

निम्नलिखित के गुणनखण्ड कीजिए

(i) a^{2} – 4

(ii) a^{2} – 49b^{2}

(iii) p^{3} – 121p

(iv) (a – b)^{2} – c^{2}

(v) a^{4} – b^{4}

(vi) 5x^{3} – 125x

(vii) 63a^{2} – 112b^{2}

(viii) 9x^{2}y^{2} – 16

(ix) (l+ m) – (l – m)^{2}

हल:

(i) a^{2} – 4

a^{2} – 4 = (a)^{2} – (2)^{2}

= (a – 2) (a + 2)

(ii) a^{2} – 49b^{2}

a^{2} – 49b^{2} = (a)^{2}(7b)^{2}

= (a – 7b) (a + 7b)

(iii) p^{3} – 121p

p^{3} – 121p =p (p^{2} – 121)

=p {(p^{2}– (11)^{2}}

= p (p – 11) (p + 11)

(iv) (a – b)^{2} – c^{2}

(a – b)^{2} – c^{2}

= (a – b – c) (a – b + c)

(v) a^{4} – b^{4}

a^{4} – b^{4}

= (a^{2})^{2} – (b^{2})^{2}

= (a^{2} – b^{2}) (a^{2} + b^{2})

= (a – b) (a + b) (a^{2} + b^{2})

(vi) 5x^{3} – 125x

5x^{3} – 125x

= 5 (x^{2 }– 25)

= 5x (x^{2} – 5^{2})

= 5x (x – 5) (x + 5)

(vii) 63a^{2} – 112b^{2}

63a^{2} – 112b^{2}

=7 (9a^{2} – 16b^{2})

= 7 {(3a)^{2} – (4b)^{2}}

= 7(3a – 4b) (3a + 4b)

(viii) 9x^{2}y^{2} – 16

9x^{2}y^{2} – 16 = (3xy)^{2} – (4)^{2}

= (3xy – 4) (3xy + 4)

(ix) (l + m)^{2} – (l – m)^{2}

(l + m)^{2} – (l – m)

= {(l + m) + (l – m)} {(l + m) + (l – m)}

= (l + m – l + m) (l + m + l – m)

= (2m) (2l)

= 4lm

प्रश्न 2

निम्नलिखित के गुणनखण्ड कीजिए

(i) lx^{2} + mx

(ii) 2x^{3} + 2xy^{2} + 2xz^{2}

(iii) a(a + b) + 4 (a + b)

(iv) (xy + y) + x +1

(v) 5a^{2} – 15a – 6c + 2ac

(vi) am^{2} + bm^{2} + bn^{2}+ an^{2}

हल:

(i) lx^{2} + mx

lx^{2} + mx

= x (lx + m)

(ii) 2x^{3} + 2xy^{2} + 2xz^{2}

2x^{3} + 2xy^{2} +2xz^{2}

= 2x (x^{2} + y^{2} + z^{2})

(iii) a(a + b) + 4 (a + b)

a(a + b) + 4 (a + b)

= (a + b)(a + 4)

(iv) (xy + y) + x + 1

(xy + y) + (x + 1)

= y (x + 1) + 1 (x + 1)

= (x + 1) (y + 1)

(v) 5a^{2} – 15a – 6c + 2ac

5a – 15a – 6c + 2ac

= 5a^{2} – 15a + 2ac – 6c

= 5a (a – 3) + 2c (a – 3)

= (a – 3) (5a + 2c)

(vi) am^{2} + bm^{2} + bn^{2} + an^{2}

am^{2} + bm^{2} + bn^{2} + an^{2}

= am^{2} + bm^{2} + an^{2} + bn^{2}

= m^{2} (a + b) + n^{2} (a + n)

= (a + b) (m^{2} + n^{2})

प्रश्न 3

निम्नलिखित व्यंजकों के गुणनखण्ड कीजिए

(i) x^{2} + 5x + 6

(ii) q^{2} + 11q + 24

(iii) m^{2} – 10m + 21

(iv) x^{2} + 6x – 16

(v) x^{2} – 7x – 18

(vi) k^{2} – 11k – 102

(vii) y^{2} + 2y – 48.

(viii) d^{2} – 4d – 45

(ix) m^{2} + 16m + 63

(x) n^{2} – 19n – 92

(xi) p^{2} – 10p + 16

(xii) x^{2} + 4x – 45

हल:

(i) x^{2} + 5x + 6

x^{2} + 5x + 6

= x^{2} + 2x + 3x + 6

= x (x + 2) + 3(x + 2)

= (x + 2) (x + 3)

(ii) q^{2} + 11q + 24

q^{2} + 11q + 24

= q^{2} + 3q + 8q + 24

= q (q + 3) + 8 (q + 3)

= (q + 3) (q + 8)

(iii) m^{2} – 10m + 21

m^{2} – 10m + 21

= m^{2} – 3m – 7m + 21

= m (m – n) – 7 (m – 3)

= (m – 3) (m – 7)

(iv) x^{2} + 6x – 16

x^{2} + 6x – 16

= x^{2} + 8x – 2x – 16

= x (x + 8) – 2 (x + 8)

= (x + 8) (x – 2)

(v) x^{2} – 7x – 18

x^{2} – 7x – 18

= x^{2} – 9x + 2x – 18

= x (x – 9) + 2 (x – 9)

= (x – 9) (x + 2)

(vi) k^{2} – 11k – 102

k^{2} – 11k – 102

=k^{2} – 17k + 6k – 102

=k (k – 17) + 6 (k – 17)

= (k – 17) (k + 6)

(vii) y^{2} + 2y – 48

y^{2} + 2y – 48

= y^{2} + 8y – 6y – 48

= y (y + 8) – 6 (y + 8)

= (y + 8) (y – 6)

(viii) d^{2} – 4d – 45

= d^{2} – 4d – 45

= d^{2} – 9d + 5d – 45

= d (d – 9) + 5 (d – 9)

= (d – 9) (d + 5)

(ix) m^{2} + 16m + 63

m^{2} + 16m + 63

= m^{2} + 9m + 7m + 63

= m (m + 9) + 7 (m + 9)

= (m + 9) (m + 7)

(x) n^{2} – 19n – 92

n^{2} – 19n – 92

= n^{2} – 23n + 4n – 92

= n (n – 23) + 4 (n – 23)

= (n – 23) (n + 4)

(xi) p^{2} – 10p + 16

p^{2} – 10p + 16

= p^{2} – 8p – 2p + 16

= p (p – 8) – 2(p – 8)

= (p – 8) (p – 2)

(xii) x^{2} + 4x – 45

x^{2} + 4x – 45

= x^{2} + 9x – 5x – 45

= x (x + 9) – 5(x + 9)

= (x + 9) (x – 5)

We hope the RBSE Solutions for Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.2 will help you. If you have any query regarding Rajasthan Board RBSE Class 8 Maths Chapter 10 गुणनखण्ड Exercise 10.2, drop a comment below and we will get back to you at the earliest.

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