{"id":20479,"date":"2023-11-16T15:34:00","date_gmt":"2023-11-16T10:04:00","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=20479"},"modified":"2023-11-17T17:47:22","modified_gmt":"2023-11-17T12:17:22","slug":"ap-board-8th-class-maths-solutions-chapter-11-ex-11-4-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-board-8th-class-maths-solutions-chapter-11-ex-11-4-in-telugu\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 Ex 11.4"},"content":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions<\/a> Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 Ex 11.4 Textbook Exercise Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 11th Lesson \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 Exercise 11.4<\/h2>\n

1. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c38\u0c2e\u0c38\u0c4d\u0c2f\u0c32\u0c15\u0c41 \u0c24\u0c17\u0c3f\u0c28 “\u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c28\u0c41” (Identities) \u0c38\u0c42\u0c1a\u0c3f\u0c02\u0c1a\u0c3f\u0c02\u0c26\u0c3f. \u0c32\u0c2c\u0c4d\u0c27\u0c2e\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f.<\/span><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(3k + 4l) (3k +4l)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (3k + 4l)2<\/sup> \u0c07\u0c26\u0c3f (a + b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n= (3k)2<\/sup> + 2 \u00d7 3k \u00d7 4l + (4l)2<\/sup> [\u2235 (a + b)2<\/sup> = a2<\/sup> + 2ab + b2<\/sup>]
\n= 3k \u00d7 3k + 24kl + 4l \u00d7 4l
\n= 9k2<\/sup> + 24kl + 16l2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(ax2<\/sup> + by2<\/sup>) (ax2<\/sup> + by2<\/sup>)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (ax2<\/sup> + by2<\/sup>)2<\/sup> \u0c07\u0c26\u0c3f (a + b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n= (ax2<\/sup>)2<\/sup> + 2 \u00d7 ax2<\/sup> \u00d7 by2<\/sup> + (by2<\/sup>)2<\/sup> [\u2235 (a + b)2<\/sup> = a2<\/sup> + b2<\/sup> + 2ab]
\n= ax2<\/sup> \u00d7 ax2<\/sup> + 2abx2<\/sup>y2<\/sup> + by2<\/sup> \u00d7 by2<\/sup>
\n= a2<\/sup>x4<\/sup> + 2abx2<\/sup>y2<\/sup> + b2<\/sup>y4<\/sup><\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(7d – 9e) (7d – 9e)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (7d – 9e)2<\/sup>, \u0c07\u0c26\u0c3f (a – b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n= (7d)2<\/sup> – 2 \u00d7 7d \u00d7 9e + (9e)2<\/sup> [\u2235 (a – b)2<\/sup> = a2<\/sup> – 2ab + b2<\/sup>]
\n= 7d \u00d7 7d – 126de + 9e \u00d7 9e
\n= 49d2<\/sup> – 126de + 81e2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n(m2<\/sup> – n2<\/sup>) (m2<\/sup> + n2<\/sup>)
\n\u0c38\u0c3e\u0c27\u0c28.
\n(m2<\/sup> – n2<\/sup>) (m2<\/sup> + n2<\/sup>) \u0c07\u0c26\u0c3f (a + b) (a – b) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n\u2234 (m2<\/sup> + n2<\/sup>) (m2<\/sup> – n2<\/sup>) = (m2<\/sup>)2<\/sup> – (n2<\/sup>)2<\/sup> = m4<\/sup> – n4<\/sup> [\u2235 (a + b)(a – b) = a2<\/sup> – b2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\n(3t + 9s) (3t – 9s)
\n\u0c38\u0c3e\u0c27\u0c28.
\n(3t + 9s) (3t – 9s) = (3t)2<\/sup> – (9s)2<\/sup> [\u2235 (a + b)(a – b) = a2<\/sup> – b2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\n(kl – mn) (kl + mn)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= kl \u00d7 kl – mn \u00d7 mm
\n= k2<\/sup>l2<\/sup> – m2<\/sup>n2<\/sup><\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vii)
\n(6x + 5) (6x + 6)
\n\u0c38\u0c3e\u0c27\u0c28.
\n(6x + 5) (6x + 6)
\n\u0c07\u0c26\u0c3f (ax + b) (ax + c) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(ax + b) (ax + c) = a2<\/sup>x2<\/sup> + ax (b + c) + bc
\n(6x + 5) (6x + 6) = (6)2<\/sup>x2<\/sup> + 6x (5 + 6) +5 \u00d7 6
\n= 36x2<\/sup> + 6x \u00d7 11 + 30
\n= 36x2<\/sup> + 66x + 30<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (viii)
\n(2b – a) (2b + c)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c07\u0c26\u0c3f (ax – b) (ax + c) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(ax – b) (ax + c) = a2<\/sup>x2<\/sup> + ax (c – b) – cb
\n(2b – a) (2b + c) = (2)2<\/sup>b2<\/sup> + 2b (c – a) – ca
\n= 4b2<\/sup> + 2bc – 2ab – ca<\/p>\n

\"AP<\/p>\n

2. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c1f\u0c3f\u0c15\u0c3f \u0c24\u0c17\u0c3f\u0c28 \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c02\u0c1a\u0c3f \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f.<\/span><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n3042<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (300 + 4)2<\/sup>, \u0c07\u0c26\u0c3f (a + b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(a + b)2<\/sup> = a2<\/sup> + 2ab + b2<\/sup>
\na = 300, b = 4
\n(300 + 4)2<\/sup> = (300)2<\/sup> + 2 \u00d7 300 \u00d7 4 + (4)2<\/sup>
\n= 300 \u00d7 300 + 24000 + 4 \u00d7 4
\n= 90,000 + 2400 + 16 = 92,416<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n5092<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (500 + 9)2<\/sup> a = 500, b = 9
\n= (500)2<\/sup> + 2 \u00d7 500 \u00d7 9 + (9)2<\/sup>
\n= 500 \u00d7 5000 + 9000 + 9 \u00d7 9
\n= 2,50,000 + 90000 + 81
\n= 2,59,081<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n9922<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (1000 – 8)2<\/sup> a = 1000, b = 8
\n= (1000)2<\/sup> – 2 \u00d7 1000 \u00d7 8 + (8)2<\/sup>
\n= 10000 \u00d7 1000 – 16,000 + 8 \u00d7 8
\n= 10,00,000 – 16000 + 64
\n= 10,00,064 – 1600
\n= 9,98,464<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n7992<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (800 – 1)2<\/sup> a = 800, b = 1
\n= (800)2<\/sup> – 2 \u00d7 800 \u00d7 1 + (1)2<\/sup>
\n= 800 \u00d7 800 – 1600 + 1
\n= 6,40,000 – 1600 + 1
\n= 6,40,001 – 1600
\n= 6,38,401<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\n304 \u00d7 296
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (300 + 4) (300 – 4),
\n\u0c07\u0c26\u0c3f (a + b) (a – b) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(a + b) (a – b) = a2<\/sup> – b2<\/sup>
\n(300 + 4) (300 – 4) = (300)2<\/sup> – (4)2<\/sup>
\n=300 \u00d7 300 – 4 \u00d7 4
\n= 90,000 – 16
\n= 89,984<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\n83 \u00d7 77
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (80 + 3) (80 – 3)
\n= (80)2<\/sup> – (3)2<\/sup> [\u2235 (a + b) (a – b) = a2<\/sup> – b2<\/sup>]
\n= 80 \u00d7 80 – 3 \u00d7 3
\n= 6400 – 9
\n= 6391<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vii)
\n109 \u00d7 108
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (100 + 9) (100 + 8)
\n= (100) + (9 + 8) 100 + 9 \u00d7 8
\n= 10,000 + 1700 + 72
\n= 11,772<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (viii)
\n204 \u00d7 206
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (205 – 1) (205 + 1)
\n= (205)2<\/sup> – (1)2<\/sup>
\n= 205 \u00d7 205 – 1 x 1
\n= 42,025 – 1
\n= 42,024<\/p>\n","protected":false},"excerpt":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 Ex 11.4 Textbook Exercise Questions and Answers. AP State Syllabus 8th Class Maths Solutions 11th Lesson \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 Exercise 11.4 1. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c38\u0c2e\u0c38\u0c4d\u0c2f\u0c32\u0c15\u0c41 \u0c24\u0c17\u0c3f\u0c28 “\u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c28\u0c41” (Identities) \u0c38\u0c42\u0c1a\u0c3f\u0c02\u0c1a\u0c3f\u0c02\u0c26\u0c3f. \u0c32\u0c2c\u0c4d\u0c27\u0c2e\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f. \u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i) (3k + 4l) (3k +4l) \u0c38\u0c3e\u0c27\u0c28. = (3k + 4l)2 \u0c07\u0c26\u0c3f (a + … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/20479"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=20479"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/20479\/revisions"}],"predecessor-version":[{"id":20480,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/20479\/revisions\/20480"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=20479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=20479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=20479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}