{"id":44393,"date":"2022-05-30T19:00:00","date_gmt":"2022-05-30T13:30:00","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=44393"},"modified":"2023-01-25T11:36:53","modified_gmt":"2023-01-25T06:06:53","slug":"ml-aggarwal-class-8-solutions-for-icse-maths-chapter-11-ex-11-3","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/ml-aggarwal-class-8-solutions-for-icse-maths-chapter-11-ex-11-3\/","title":{"rendered":"ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.3"},"content":{"rendered":"
Question 1. (ii) 36p2<\/sup> – 60pq + 25q2<\/sup> (iii) 9x2<\/sup> + 66xy + 121 y2<\/sup> (iv) a4<\/sup> + 6a2<\/sup>b2<\/sup> + 9b4<\/sup> (v) x2<\/sup> + \\(\\frac{1}{x^{2}}\\) + 2 (vi) x2<\/sup> + x + \\(\\frac{1}{4}\\) Factorise the following (2 to 13) expressions: (ii) 4x2<\/sup> – 169y2<\/sup> Question 3. Question 4. Question 5. (ii) 1 – (b – c)2<\/sup> Question 6. (ii) (2m + 3n)2<\/sup> – (3m + 2n)2<\/sup> Question 7. (ii) 9 (3x + 2)2<\/sup> – 4 (2x – 1)2<\/sup> Question 8. (ii) 63p2<\/sup>q2<\/sup> – 7 Question 9. (ii) 9 (a + b)3<\/sup> – 25 (a + b) Question 10. (ii) p2<\/sup> – 4pq + 4q2<\/sup> – r2<\/sup> Question 11. (ii) 4a2<\/sup> – 4b2<\/sup> + 4a + 1 Question 12. (ii) 5y5<\/sup> – 405y Question 13.
\nFactorise the following expressions using algebraic identities:
\n(i) x2<\/sup> – 12x + 36
\n(ii) 36p2<\/sup> – 60pq + 25q2<\/sup>
\n(iii) 9y2<\/sup> + 66xy + 121y2<\/sup>
\n(iv) a4<\/sup> + 6a2<\/sup>b2<\/sup> + 9b4<\/sup>
\n(v) x2<\/sup> + \\(\\frac{1}{x^{2}}\\) + 2
\n(vi) x2<\/sup> + x + \\(\\frac{1}{4}\\)
\nSolution:
\nUsing (a + b)2<\/sup> = a2<\/sup> + 2ab +b2<\/sup> and (a – b)2<\/sup> = a2<\/sup> – 2ab + b2<\/sup>
\n(i) y2<\/sup> – 12x + 36
\n= (x)2<\/sup> – 2 \u00d7 x \u00d7 6 + (6)22<\/sup>
\n= (x – 6)2<\/sup><\/p>\n
\n= (6p)2<\/sup> – 2 \u00d7 6p \u00d7 5q + (5q)2<\/sup>
\n= (6p – 5q)2<\/sup><\/p>\n
\n= (3x)2<\/sup> + 2 \u00d7 3x \u00d7 11y + (11y)2<\/sup>
\n= (3x + 11 y)2<\/sup><\/p>\n
\n= (a2<\/sup>)2<\/sup> + 2 \u00d7 2a2<\/sup> \u00d7 3b2<\/sup> + (3b2<\/sup>)2<\/sup>
\n= (a2<\/sup> + 3b2<\/sup>)2<\/sup><\/p>\n
\n<\/p>\n
\n<\/p>\n
\n<\/strong>Question 2.
\n(i) 4p2<\/sup> – 9
\n(ii) 4x2<\/sup> – 169y2<\/sup>
\nSolution:
\n(i) 4p2<\/sup> – 9
\n= (2p)2<\/sup> – (3)2<\/sup>
\n= (2p + 3) (2p – 3)<\/p>\n
\n= (2x)2<\/sup> – (13y)2<\/sup>
\n= (2x + 13y) (2x – 13y)<\/p>\n
\n(i) 9x2<\/sup>y2<\/sup> – 25
\n(ii) 16x2<\/sup> – \\(\\frac{1}{144}\\)
\nSolution:
\n(i) 9x2<\/sup>y2<\/sup> – 25
\n= (3xy)2<\/sup> – (5)2<\/sup>
\n= (3xy + 5) (3xy – 5)
\n<\/p>\n
\n(i) 20x2<\/sup> – 45y2<\/sup>
\n(ii) \\(\\frac{9}{16}\\) – 25a2<\/sup>b2<\/sup>
\nSolution:
\n(i) 20x2<\/sup> – 45y2<\/sup>
\n= 5 (4x2<\/sup> – 9y2<\/sup>)
\n= 5[(2x)2<\/sup> – (3y)2<\/sup>]
\n= 5 (2x + 3y) (2x – 3y)
\n<\/p>\n
\n(i) (2a + 3b)2<\/sup> – 16c2<\/sup>
\n(ii) 1 – (b – c)2<\/sup>
\nSolution:
\n(i) (2a + 3b)2<\/sup> – 16c2<\/sup>
\n= (2a + 3b)2<\/sup> – (4c)2<\/sup>
\n= (2a + 3b + 4c) (2a + 3b – 4c)<\/p>\n
\n= (1)2<\/sup> – (b – c)2<\/sup>
\n= [1 + b – c)] [1 – (b – c)]
\n= (1 +b – c)(1 – b + c)<\/p>\n
\n(i) 9 (x + y)2<\/sup> – x2<\/sup>
\n(ii) (2m + 3n)2<\/sup> – (3m + 2n)2<\/sup>
\nSolution:
\n(i) 9 (x + x)2<\/sup> – x2<\/sup>
\n= [3 (x + y)]2<\/sup> – [x]2<\/sup>
\n= [3 (x + y) + x] [3 (x + y) – x]
\n= (3x + 3y + x) (3x + 3y – x)
\n= (4x + 3y) (2x + 3x)<\/p>\n
\n= (4m2<\/sup> + 9n2<\/sup> + 12mn) – (9m2<\/sup> + 4n2<\/sup> + 12mn)
\n= 4m2<\/sup> + 9n2<\/sup> + 12mn – 9m2<\/sup> – 4m2<\/sup> – 12mn
\n= 4m2<\/sup> + 9n2<\/sup> – 9m2<\/sup> – 4n2<\/sup>
\n= – 5m2<\/sup> + 5n2<\/sup> = 5 (n2<\/sup> – m2<\/sup>)
\n= 5 (m + n) (n – m)<\/p>\n
\n(i) 25 (a + b)2<\/sup> – 16 (a – b)2<\/sup>
\n(ii) 9 (3x + 2)2<\/sup> – 4 (2x – 1)2<\/sup>
\nSolution:
\n(i) 25 (a + b)2<\/sup> – 16 (a – b)2<\/sup>
\n= [5 (a + b)]2<\/sup> – [4 (a – b)]2<\/sup>
\n= (5a + 5b)2<\/sup> – (4a – 4b)2<\/sup>
\n= [(5a + 5b)2<\/sup> + (4a – 4b)] [(5a + 5b) – (4a – 4b)]
\n= (5a + 5b + 4a – 4b) (5a + 5b – 4a + 4b)
\n= (9a + ft) (a + 9ft)<\/p>\n
\n= [3 (3x + 2)]2<\/sup> – [2 (2x – 1)]2<\/sup>
\n= (9x + 6)2<\/sup> – (4x – 2)2<\/sup>
\n= [(9x + 6) + (4x – 2)] [(9x + 6) – (4x – 2)]
\n= (9x + 6 + 4x – 2) (9x + 6 – 4x + 2)
\n= (13x + 4) (5x + 8)<\/p>\n
\n(i) x3<\/sup> – 25x
\n(ii) 63p2<\/sup>q2<\/sup> – 7
\nSolution:
\n(i) x3<\/sup> – 25x
\n= x (x2<\/sup> – 25) = x [(x)2<\/sup> – (5)2<\/sup>]
\n= x (x + 5) (x – 5)<\/p>\n
\n= 7 (9p2<\/sup>q2<\/sup> – 1)
\n= 7 [(3pq)2<\/sup> – (1)2<\/sup>]
\n= 7 (3pq + 1) (3pq – 1)<\/p>\n
\n(i) 32a2<\/sup>b – 72b3<\/sup>
\n(ii) 9 (a + b)3<\/sup> – 25 (a + b)
\nSolution:
\n(i) 32 a2<\/sup>b – 72b3<\/sup>
\n= 8b (4a2<\/sup> – 9b2<\/sup>) \u21d2 8b [(2a)2<\/sup> – (3b)2<\/sup>]
\n= 8b (2a + 3b) (2a – 3b)<\/p>\n
\n= (a + b) [9 (a + b)2<\/sup> – 25]
\n= (a + b) [{3 (a + b)}2<\/sup> – (5)2<\/sup>]
\n= (a + 6) [(3a + 3b)2<\/sup> – (5)2<\/sup>]
\n= (a + b) [(3a + 3b + 5) (3a + 36 – 5)]
\n= (a + b) (3a + 3b + 5) (3a + 3b – 5)<\/p>\n
\n(i) x2<\/sup> – y2<\/sup> – 2y – 1
\n(ii) p2<\/sup>– 4pq + 4q2<\/sup> – r2<\/sup>
\nSolution:
\n(i) x2<\/sup> – y2<\/sup> – 2y – 1
\n= x2<\/sup> – (y2<\/sup> + 2y + 1)
\n= (x)2<\/sup> – (y + 1)2<\/sup>
\n= [x + (y + 1)] [x – (y + 1)]
\n= (x + y + 1)(x – y – 1)<\/p>\n
\n= (p)2<\/sup> – 2 \u00d7 p \u00d7 2q + (2q)2<\/sup> – r2<\/sup>
\n{\u2235 (a – b)2<\/sup> = a2 – 2ab + b2<\/sup>
\na2<\/sup> – b2<\/sup> = (a + b)(a – b)}
\n= (p – 2q)2<\/sup> – (r)2<\/sup>
\n= (p – 2q + r)(p – 2q – r)<\/p>\n
\n(i) 9x2<\/sup> – y2<\/sup> + 4y – 4
\n(ii) 4a2<\/sup> – 4b2<\/sup> + 4a + 1
\nSolution:
\n(i) 9x2<\/sup> – y2<\/sup> + 4y – 4
\n= 9x2<\/sup> – (y2<\/sup> – 4y + 4)
\n= 9x2<\/sup> – (y – 2)2<\/sup>
\n= (3x)2<\/sup> (y – 2)2<\/sup>
\n= {3x + (y – 2)} {3x – (y – 2)}
\n= (3x + y – 2) (3x – y + 2)<\/p>\n
\n= (4a2<\/sup> + 4a + 1) – 4b2<\/sup>
\n= (2a + 1)2<\/sup> – (2b)2<\/sup>
\n= (2a + 2b + 1) (2a – 2b + 1)<\/p>\n
\n(i) 625 – p4<\/sup>
\n(ii) 5y5<\/sup> – 405y
\nSolution:
\n(i) 625 – p4<\/sup>
\n= (25)2<\/sup> – (p2<\/sup>)2<\/sup>
\n= (25 + p2<\/sup>) (25 – p2<\/sup>)
\n= (25 + p2<\/sup>) [(5)2<\/sup> – (p)2<\/sup>]
\n= (25 +p2<\/sup>) (5 + p) (5 – p)<\/p>\n
\n= 5y(y4<\/sup> – 81)
\n= 5y [(y2<\/sup>)2<\/sup> – (9)2<\/sup>]
\n= 5y (y2<\/sup> + 9) (y2<\/sup> – 9)
\n= 5y (y2<\/sup> + 9) [(y)2<\/sup> – (3)2<\/sup>
\n= 5y (y2<\/sup> + 9) (y + 3) (y – 3)<\/p>\n
\n(i) x4<\/sup> – y4<\/sup> + x2<\/sup> – y2<\/sup>
\n(ii) 64a2<\/sup> – 9b2<\/sup> + 42bc – 49c2<\/sup>
\nSolution:
\n(i) x4<\/sup> – y4<\/sup> + x