{"id":27423,"date":"2020-07-01T08:31:11","date_gmt":"2020-07-01T03:01:11","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=27423"},"modified":"2021-07-02T15:07:09","modified_gmt":"2021-07-02T09:37:09","slug":"kseeb-solutions-for-class-8-maths-chapter-4-additional-questions","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-8-maths-chapter-4-additional-questions\/","title":{"rendered":"KSEEB Solutions for Class 8 Maths Chapter 4 Factorisation Additional Questions"},"content":{"rendered":"

Students can Download Maths Chapter 4 Factorisation Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka State Syllabus Class 8 Maths Chapter 4 Factorisation Additional Questions<\/h2>\n

Question 1.
\nChoose the correct answer
\n(a) 4a + 12b is equal to
\nA. 4a
\nB. 12b
\nC. 4(a + 3b)
\nD. 3a
\nAnswer:
\n(C) 4 (a + 3b)<\/p>\n

\"KSEEB<\/p>\n

(b) The product of two numbers is positive and their sum is negative only when
\nA. both are positive
\nB. both are negative
\nC. one positive other negative
\nD. one of them is equal to zero
\nAnswer:
\n(B) both are negative<\/p>\n

(c) Factorising x2<\/sup> + 6x + 8 we get
\nA. (x + 1) (x + 8)
\nB. (x + 6) (x + 2)
\nC. (x + 10) (x – 2)
\nD. (x + 4) (x + 2)
\nAnswer:
\n(D) (x + 4) (x + 2)<\/p>\n

(d) The denominator of an algebraic fraction should not be
\nA. 1
\nB. 0
\nC. 4
\nD. 7
\nAnswer:
\n(B) 0<\/p>\n

(e) If the sum of two integers is – 2 and their proiduct is – 24, the numbers are
\nA. 6 and 4
\nB. – 6 and 4
\nC. – 6 and -4
\nD. 6 and – 4
\nAnswer:
\n(B) – 6 and 4<\/p>\n

(f) The difference (0.7)2<\/sup> – (0.3)2<\/sup> simplifies to
\nA. 0.4
\nB. 0.04
\nC. 0.49
\nD. 0.56
\nAnswer:
\n(A) 0.4<\/p>\n

\"KSEEB<\/strong><\/p>\n

Question 2.
\nFactorise the following
\n(i) x2<\/sup> + 6x + 9
\nAnswer:
\nx2<\/sup> + 6x + 9
\n= x2<\/sup> + 2.x.3 + 32<\/sup>
\n= (x + 3)2<\/sup><\/p>\n

(ii) 1 – 8x + 16x2<\/sup>
\nAnswer:
\n1 – 8x + 16x2<\/sup>
\n= 12<\/sup> – 2.1.4x + (4x)2<\/sup>
\n= (1 – 4x)2<\/sup><\/p>\n

(iii) 4x2 <\/sup>– 81y2<\/sup>
\nAnswer:
\n4x2<\/sup> – 81 y2<\/sup>
\n= (2x)2<\/sup> – ( 9y)2<\/sup>
\n= (2x + 9y) (2x – 9y)<\/p>\n

(iv) 4a2<\/sup> + 4ab + b2<\/sup>
\nAnswer:
\n4a2<\/sup> + 4ab + b2<\/sup>
\n= (2a)2<\/sup> +2.2a.b + b2<\/sup>
\n= (2a + b)2<\/sup><\/p>\n

(v) a2<\/sup>b2<\/sup> + c2<\/sup>d2<\/sup> – a2<\/sup>c2<\/sup> – b2<\/sup>d2<\/sup>
\nAnswer:
\na2<\/sup>b2<\/sup> + c2<\/sup>d2<\/sup> – a2<\/sup>c2<\/sup> – b2<\/sup>d2<\/sup>
\n= a2<\/sup>b2<\/sup> – a2<\/sup>c2<\/sup> + c2<\/sup>d2<\/sup> – b2<\/sup>d2<\/sup>
\n= a2<\/sup> (b2<\/sup> – c2<\/sup>) – d2<\/sup> (b2<\/sup> – c2<\/sup>)
\n= (b2<\/sup> – c2<\/sup>) (a2<\/sup> – d2<\/sup>)<\/p>\n

\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nFactorise the following
\n(i) x2<\/sup> + 7x + 12
\nAnswer:
\nx2<\/sup> + 7x + 12 12xz
\nx2<\/sup> + 4x + 3x + 12<\/p>\n

x (x + 4) + 3 (x + 4)
\n(x + 4) (x + 3)<\/p>\n

\"KSEEB<\/p>\n

(ii) x2<\/sup> + x – 12
\nAnswer:
\nx2<\/sup> + 4x – 3x – 12
\nx(x + 4) -3 (x + 4)
\n(x + 4) (x – 3)<\/p>\n

\"KSEEB<\/p>\n

(iii) x2<\/sup> – 3x – 18
\nAnswer:
\nx2<\/sup> – 6x + 3x – 18
\nx(x – 6) +3 (x -6)
\n(x – 6) (x + 3)<\/p>\n

\"KSEEB<\/p>\n

(iv) x2<\/sup> + 4x – 21
\nAnswer:
\nx2<\/sup> + 7x – 3x – 12
\nx(x + 7) -3 (x + 7)
\n(x + 7) (x – 3)<\/p>\n

\"KSEEB<\/p>\n

(v) x2<\/sup> – 4x – 192
\nAnswer:
\nx2<\/sup> – 16x + 12x – 192
\nx(x – 16) +12 (x – 16)
\n(x -16) (x +12)<\/p>\n

\"KSEEB<\/p>\n

(vi) x4<\/sup> – 5x2<\/sup> + 4
\nAnswer:
\nx4<\/sup> – 4x2<\/sup> – x2<\/sup> + 4
\nx2<\/sup>(x2<\/sup> – 4) -1 (x2<\/sup> – 4)
\n(x2<\/sup> – 4) (x2<\/sup> – 1) = (x + 2) (x – 2)
\n(x + 1) (x – 1)<\/p>\n

\"KSEEB<\/p>\n

(vii) x4<\/sup> – 13x2<\/sup>y2<\/sup> + 36y4<\/sup>
\nAnswer:
\nx4<\/sup> -9x2<\/sup>y2<\/sup> – 4x2<\/sup>y2<\/sup> +36y4<\/sup>
\nx2<\/sup>(x2<\/sup> – 9y2<\/sup>) -4y2<\/sup>
\n(x2<\/sup> – 9y2<\/sup>)
\n(x2<\/sup> – 9y2<\/sup>) (x2<\/sup> – 4y2<\/sup>)
\n= [x2<\/sup> – (3y)2<\/sup>] [x2<\/sup> – (2y)2<\/sup>]
\n= (x + 3y) (x – 3y) (x + 2y) (x – 2y)<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nFactorise the following
\n(i) 2x2<\/sup> + 7x + 6
\nAnswer:
\n2x2<\/sup> + 4x + 3x + 6
\n2x (x +2) + 3 (x + 2)
\n(x + 2) (2x + 3)<\/p>\n

\"KSEEB<\/p>\n

(ii) 3x2<\/sup> – 17x + 20
\nAnswer:
\n3x2<\/sup> – 12x – 5x + 20
\n3x (x – 4) – 5 (x – 4)
\n(x – 4) (3x – 5)<\/p>\n

(iii) 6x2<\/sup> – 5x – 14
\nAnswer:
\n6x2<\/sup> – 12x + 7x – 14
\n6x (x – 2) + 7 (x – 2)
\n(x – 2) (6x +7)
\n\"KSEEB<\/p>\n

(iv) 4x2<\/sup> + 12xy – 5y2<\/sup>
\nAnswer:
\n4x2<\/sup> – lOxy + 2xy + 5y2<\/sup> – 20x2<\/sup>y2<\/sup>
\n2x (2x + 5y) + y
\n(2x + 5y)
\n(2x + 5y) (2x + y)
\n\"KSEEB<\/p>\n

(v) 4x4<\/sup> – 5x2<\/sup> + 1
\nAnswer:
\n4x2<\/sup> – 4x2<\/sup> – x2<\/sup> + 1 4×4
\n4x2<\/sup> (x2<\/sup> – 1) – 1
\n(x2<\/sup> – 1)
\n(x2<\/sup> – 1) (4x2<\/sup> – 1)
\n(x2<\/sup> – 12<\/sup>) – ((2x)2<\/sup> – 12<\/sup>)
\n(x2<\/sup> – l2<\/sup>) – ((2x)2<\/sup> – l2<\/sup>)
\n(x + 1) (x – 1) (2x + 1) (2x – 1)
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nFactorise the following
\n(i) x8<\/sup> – y8<\/sup>
\nAnswer:
\n(x4<\/sup>)2<\/sup> – (y4<\/sup>)2<\/sup>
\n= (x4<\/sup> + y4<\/sup>) (x4<\/sup> – y4<\/sup>)
\n= (x4<\/sup> + y4<\/sup>) [(x2<\/sup>)2<\/sup> – (y2<\/sup>)2<\/sup>]
\n= (x4<\/sup> + y4<\/sup>) (x2<\/sup> + y2<\/sup>) (x2<\/sup> – y2<\/sup>)
\n= (x4<\/sup> + y4<\/sup>) (x2<\/sup> + y2<\/sup>) (x + y)
\n(x – y)<\/p>\n

(ii) a12<\/sup>x4<\/sup> – a4<\/sup>x12<\/sup>
\nAnswer:
\n[(a6<\/sup>)2<\/sup>(x2<\/sup>)2<\/sup> – (a2<\/sup>)2<\/sup>(x6<\/sup>)2<\/sup>]
\n= [(a6x2<\/sup>)2 – (a2<\/sup>x6)2]
\n= (a6x2<\/sup> + a2x6) (a6x2 – a2x6)
\n= a2<\/sup>x2<\/sup> (a4<\/sup> + x4<\/sup>)
\n[(a3<\/sup>)2<\/sup> x2<\/sup> – a2<\/sup> (x3<\/sup>)2<\/sup>]
\n= a2<\/sup>x2<\/sup> (a4<\/sup> + x4<\/sup>) [(a3<\/sup>x)2<\/sup> – (ax3)2] = a2x2 (a4<\/sup> + x4<\/sup>) [(a3x + ax3<\/sup>)
\n(a3<\/sup>x – ax3<\/sup>)]
\n= a2<\/sup>x2<\/sup> (a4<\/sup> + x4<\/sup>) [ax(a2<\/sup> + x2<\/sup>).ax (a2<\/sup> – x2<\/sup>)]
\n= a2<\/sup>x2<\/sup> (a4<\/sup> + x4<\/sup>) [a2<\/sup>x2<\/sup> (a2<\/sup> + x2<\/sup>) (a2<\/sup> – x2<\/sup>)]
\n= a4<\/sup>x4<\/sup> (a4<\/sup> + x4<\/sup>) (a2<\/sup> + x2<\/sup>) (a + x) (a – x)<\/p>\n

(iii) x4<\/sup> + x2<\/sup> + 1
\nAnswer:
\nX4<\/sup> + X2<\/sup> + 1 + X2<\/sup> – X2<\/sup>
\n= x4<\/sup> + 2x2<\/sup> + 1 – x2<\/sup>
\n= (x2<\/sup>)2<\/sup> + 2.x2<\/sup>.1 + l2<\/sup> – x2<\/sup>
\n= (x2<\/sup> + l)2<\/sup> – X2<\/sup>
\n= (x2<\/sup> + 1 + x) (x2<\/sup> + 1 – x)
\n= (x2<\/sup> + x + 1) (x2<\/sup> – X + 1)<\/p>\n

(iv) x4<\/sup> + 5x2<\/sup> + 9
\nAnswer:
\nx4<\/sup> + 5x2<\/sup> + 9 + x2<\/sup> – x2<\/sup>
\n= x4<\/sup> + 6x2<\/sup> + 9 – x2<\/sup>
\n= (x2<\/sup>)2<\/sup> + 2.x2<\/sup>.3 + 32<\/sup> – x2<\/sup> = (x2<\/sup> + 3)2 – x2<\/sup>
\n= (x2<\/sup> + 3 + x) (x2<\/sup> + 3 – x)
\n= (x2<\/sup> + x + 3) (x2<\/sup> – x + 3)<\/p>\n

\"KSEEB<\/strong><\/p>\n

Question 6.
\nFactorise x4<\/sup> + 4y4<\/sup> use this to prove that 2011 4 + 64 is a composite number Answer:
\nx4<\/sup> + 4y4<\/sup>
\n= (x2<\/sup>)2<\/sup> + (2y2<\/sup>)2<\/sup>
\n= (x2<\/sup> + 2y2<\/sup>)2<\/sup> – 2x2<\/sup>.2y2<\/sup>
\n[v a2<\/sup> + b2<\/sup> = (a + b)2<\/sup> – 2ab]
\n= (x2<\/sup> + 2y2<\/sup>) – (4x2<\/sup>y2<\/sup>)
\n= (x2<\/sup> + 2y2<\/sup>) – (2xy)2<\/sup>
\n(x2<\/sup> + 2y2<\/sup> + 2xy) (x2<\/sup> + 2y2<\/sup> – 2xy) [a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n\u2234 x4<\/sup> + 4y4<\/sup> = (x2<\/sup> + 2y2<\/sup> + 2xy)
\n(x2<\/sup> + 2y2<\/sup> – 2xy)
\nSimilarly 20114<\/sup> + 64 can be written as
\n20114<\/sup> + 4 x 16 = (2011)4<\/sup> + 4.24<\/sup>
\n= (20112<\/sup> + 2.22<\/sup> + 2.2011.2) (20112<\/sup> + 2.22<\/sup> – 2.2011.2)
\n\u2234 20114<\/sup> + 64 is a composite number.<\/p>\n

\"KSEEB<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 4 Factorisation Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 8 Maths Chapter 4 Factorisation Additional Questions Question 1. Choose the correct answer (a) 4a + …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27423"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=27423"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27423\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=27423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=27423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=27423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}