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

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 10 |

Chapter Name |
Factorization |

Exercise |
Exercise 10.2 |

Number of Questions |
3 |

Category |
RBSE Solutions |

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

Question 1.

Factorize the following expressions.

(i) a² – 4

(ii) a² – 49b²

(iii) p³ – 121p

(iv) (a – b)² – c²

(v) a^{4} – b^{4}

(vi) 5x^{3} – 125x

(vii) 63a² – 112b²

(viii) 9x²y² – 16

(ix) (l + m)² – (l – m)²

Solution:

(i) a² – 4

a² – 4

= (a)² – (2)²

= (a – 2) (a + 2)

(ii) a² – 49b²

a² – 49b²

= (a)² – (7b)²

= (a – 7b) (a + 7b)

(iii) p^{3} – 121p

p^{3} – 121p

= p(p² – 121)

= p{(p)² – (11)²}

= p(p – 11)(p + 11)

(iv) (a – b)² – c²

(a – b)² – c²

= (a – b – c) (a – b + c)

(v) a^{4} – b^{4}

a^{4} – b^{4}

= (a²)² – (b²)²

= (a² – b²) (a² + b²)

= (a – b)(RBSESolutions.com) (a + b) (a² + b²)

(vi) 5x^{3} – 125x

5x^{3} – 125x

= 5x (x² – 25)

= 5x(x² – 5²)

= 5x (x – 5) (x + 5)

(vii) 63a² – 112b²

63a² – 112b²

= 7 (9a² – 16b²)

= 7 {(3a)² – (4b)²}

= 1 (3a- 4b) (3a + 4b)

(viii) 9x²y² – 16

9x²y² – 16

= (3xy)² – (4)²

= (3xy – 4) (3xy + 4)

(ix) (l + m)² – (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)

= (2m) (2l)

= 4lm

Question 2.

Factorize the(RBSESolutions.com)following expressions.

(i) lx² + mx

(ii) 2x^{3} + 2xy² + 2xz²

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

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

(v) 5a² – 15a – 6c + 2ac

(vi) am² + bm² + bn² + an²

Solution:

(i) lx² + mx

lx² + mx

= x (lx + m)

(ii) 2x^{3} + 2xy² + 2xz²

2x^{3} + 2xy² + 2xz²

= 2x (x² + y² + z²)

(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) 5a² – 15a -6c + 2ac

5a² – 15a – 6c + 2ac

= 5a² – 15a + 2ac – 6c

= 5a (a – 3) + 2c (a – 3)

= (a – 3)(RBSESolutions.com) (5a + 2c)

(vi) am² + bm² + bn² + an²

am² + bm² + bn² + an²

= am² + bm² + an² + bn²

= m² (a + b) + n² (a + n)

= (a + b) (m² + n²)

Question 3.

Factorize the following expressions.

(i) x² + 5x + 6

(ii) q² + 11q + 24

(iii) m² – 10m + 21

(iv) x² + 6x – 16

(v) x² – 7x – 18

(vi) k² – 11k – 102

(vii) y² + 2y – 48

(viii) d² – 4d – 45

(ix) m² + 16m + 63

(x) n² – 19n – 92

(xi) p² – 10p + 16

(xii) x² + 4x – 45

Solution:

(i) x² + 5x + 6

x² + 5x + 6

= x² + 2x + 3x + 6

= x (x + 2)(RBSESolutions.com) + 3(x +2)

= (x + 2) (x + 3)

(ii) q² + 11q + 24

q² + 11q + 24

= q² + 3q + 8q + 24

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

= (q + 3) (q + 8)

(iii) m² – 10m + 21

m² – 10m + 21

= m² – 3 m – 7m + 21

= m (m – n) – 7 (m – 3)

= (m – 3) (m – 7)

(iv) x² + 6x – 16

x² + 6x – 16

= x² + 8x – 2x – 16

= x (x + 8)(RBSESolutions.com) – 2 (x + 8)

= (x + 8) (x – 2)

(v) x² – 7x – 18

x² – 7x – 18

= x² – 9x + 2x – 18

= x (x – 9) + 2 (x – 9)

= (x – 9) (x + 2)

(vi) k² – 11 k – 102

k² – 11k – 102

= k² – 17k + 6k – 102

= k (k – 17) + 6 (k – 17)

= (k – 17) (k + 6)

(vii) y² + 2y – 48

y² + 2y – 48

= y² + 8y(RBSESolutions.com)- 6y – 48

= y(y + 8) – 6(y + 8)

= (y + 8) (y – 6)

(viii) d² – 4d – 45

d² – 4d – 45

= d² – 9d + 5 d – 45

= d (d – 9) + 5 (d – 9)

= (d – 9) (d + 5)

(ix) m² + 16m + 63

m² + 16m + 63

= m² + 9m + 7m + 63

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

= (m + 9) (m + 7)

(x) n² – 19n – 9²

n² – 19n – 92

= n² – 23n(RBSESolutions.com) + 4n – 92

= n (n – 23) + 4 (n – 23)

= (n – 23) (n + 4)

(xi) p² – 10p + 16

p² – 10p + 16

= p² – 8p – 2p + 16

= p (p – 8) – 2(p – 8)

= (p – 8) (p – 2)

(xii) x² + 4x – 45

x² + 4x – 45

= x² + 9x – 5x – 45

= x (x + 9) – 5(x + 9)

= (x + 9) (x – 5)

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

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