আজকের এই পোস্টে আমরা মধ্য শিক্ষা পর্ষদের সপ্তম শ্রেণীর সমীকরণ গঠন ও সমাধান অধ্যায়ের Kose Dekhi 19.2 Class 7 সকল গণিতের সম্পূর্ণ উত্তর দিয়েছি।
যদি তোমাদের আরো ও গণিতের সমাধানের প্রয়োজন হয় তাহলে আমাদের এই ওয়েবসাইটের কমেন্ট বক্সে লিখে জানাবে। আমরা চেষ্টা করবো যত তাড়াতাড়ি তোমাদের সকল অধ্যায়ের উত্তর দিতে পারি। আর যদি কষে দেখি 19.2 Class 7 কোনো সমাধানের ভুল থাকে তাহলে কমেন্ট বক্সে অবশই জানাবেন।
Kose Dekhi 19.2 Class 7 | কষে দেখি 19.2
1 ) উৎপাদকে বিশ্লেষণ করি –
(i) x2 + 14x + 49
= x2 + (7+7)x + 49
= x2 + 7x + 7x + 49
= x (x+7) +7 (x+7)
= (x+7) (x+7)
(ii) 4m2 – 36m +81
= 4m2 – (18+18)m + 81
= 4m2 – 18m – 18m + 81
= 2m (2m-9) -9 (2m-9)
= (2m-9) (2m-9)
(iii) 25x2 + 30x + 9
= 25x2 + (15+15)x + 9
= 25x2 + 15x + 15x + 9
= 5x (5x+3) + 3(5x+3)
= (5x+3) (5x+3)
(iv) 121b2 – 88b + 16
= 121b2 – (44+44)b + 16
= 121b2 – 44b – 44b + 16
= 11b (11b-4) -4 (11b-4)
= (11b – 4) (11b – 4)
(v) (x2y)2 – 4x2y2
= (x2y)2 – (2xy)2
= (x2y + 2xy) (x2y – 2xy)
= xy(x+2) xy(x-2)
= x2y2 (x+2) (x-2)
(vi) a4 + 4a2b2 + 4b4
= a4 + (2+2)a2b2 + 4b4
= a4 + 2a2b2 + 2a2b2 + 4b4
= a2 (a2 + 2b2) + 2b2 (a2+2b2)
= (a2+2b2) (a2+2b2)
(vii) 4x2 – 16
= (2x)2 – 42
= (2x-4) (2x+4)
= 2(x-2) 2(x+2)
= 4 (x-2) (x+2)
(viii) 121 -36x2
= (11)2 – (6x)2
= (11 – 6x) (11 + 6x)
(ix) x2y2 – p2q2
= (xy)2 – (pq)2
= (xy – pq) (xy+pq)
(x) 80m2 – 125
= 5 (16m2 – 25)
= 5 {(4m)2 – 52}
= 5 (4m+5) (4m-5)
(xi) ax2 – ay2
= a (x2 – y2)
= a (x+y) (x-y)
(xii) 1- (m+n)2
= 12 – (m+n)2
= (1+m+n) (1 -m- n)
(xiii) (2a – b – c)2 – (a – 2b – c)2
= [(2a-b-c) + (a-2b-c)] [(2a-b-c) – (a-2b-c)]
= (2a – b – c + a – 2b -c) (2a -b-c – a + 2b +c)
= (3a – 3b – 2c) (a +b)
(xiv) x2 – 2xy – 3y2
= x2 – 2xy + y2 – 4y2
= (x-y)2 – (2y)2
= (x-y+2y) (x-y-2y)
= (x+y)(x-3y)
(xv) x2 + 9y2 + 6xy – z2
= x2 + 6xy + 9y2 – z2
= x2 + 2. x .3y +(3y)2 – z2
= (x+3y)2 – z2
= (x+3y+z) (x+3y-z)
(xvi) a2– b2+ 2bc – c2
= a2 – (b2 – 2bc + c2)
= a2 – (b-c)2
=(a +b-c) {a-(b-c)}
= (a+b-c) (a-b+c)
(xvii) a2 (b-c)2 – b2 (c-a)2
= {a(b-c)}2 – {b(c-a)}2
= {a(b-c) + b(c-a)} {a(b-c) – b( c-a)}
= (ab-ac +bc – ab) (ab – ac – bc +ab)
= (bc-ac) (2ab-ac –bc)
= c (b-a) (2ab-bc-ca)
(xviii) x2 – y2 – 6yz – 9z2
= x2 – (y2 + 6yz +9z2)
= x2 – {(y)2 +2. y .3z +(3z)2}
= x2 – (y+3z)2
= {x+(y+3z)} {x – ( y+3z)}
=(x+y+3z) (x-y-3z)
(xix) x2 – y2 + 4x – 4y
= (x+y)(x-y) + 4(x-y)
= (x-y) (x+y+4)
(xx) a2– b2 + c2– d2 – 2(ac-bd)
= a2 – b2 +c2 – d2 – 2ac + 2bd
= a2 -2ac +c 2 – b2 +2bd – d2
= (a2 -2ac+c2 ) – (b2 -2bd+d2)
=(a-c)2 – (b-d)2
= {(a-c) +(b-d)} {(a-c) – (b-d)}
= (a-c +b-d) (a-c-b+d)
= (a+b-c-d) (a-b-c+d)
(xxi) 2ab-a2-b2+c2
= c2– (a2– 2ab+b2)
= c2– (a-b)2
= {c+(a-b) } {c-(a-b)}
= (c+a-b)(c-a+b)
(xxii) 36x2 – 16a2 – 24ab – 9b2
= 36x2 – (16a2 +24ab +9b2)
= (6x)2 – {(4a)2+2.4a.3b+(3b)2}
= (6x)2 – (4a +3b)2
= {6x +(4a+3b) }{6x -(4a+3b)}
= (6x+4a+3b)(6x-4a -3b)
(xxiii) a2-1+2b-b2
= a2 – (b2-2b+1)
=a2 – (b-1)2
= {a+(b-1)} {a-(b-1)}
= (a+b-1) (a-b+1)
(xxiv) a2– 2a–b2+ 2b
= a2– 2a–b2+ 2b +1-1
=a2– 2a+1–b2+ 2b-1
= (a2 -2a+1) – (b2 -2b+1)
=(a-1)2 – ( b-1)2
= {(a-1)+(b-1)} {(a-1)-(b-1)}
= (a-1+b-1) (a-1-b+1)
= (a+b-2) (a-b)
(xxv) (a2-b2)(c2-d2) – 4abcd
= a2c2 –b2c2 –a2d2 +b2d2 -2abcd-2abcd
= a2c2 -2abcd +b2d2 –b2c2 -2abcd–a2d2
= {(ac)2 – 2ac.bd + (bd)2 } – {(bc)2 +2 bc.ad +(ad)2}
= (ac –bd)2 – (bc +ad)2
= {(ac –bd)+(bc +ad)} {(ac –bd) – (bc +ad)}
= (ac –bd +bc +ad) (ac-bd –bc –ad)
(xxvi) a2– b2– 4ac + 4bc
= (a+b) (a-b)-4c(a-b)
= (a-b) (a+b – 4c)
(xxvii) (a2 – b2 – c2 + d2)2 – 4(ad – bc)2
= {a2 – b2 – c2 + d2 – 2(ad – bc)} { a2 – b2 – c2 + d2 + 2(ad – bc)}
= {a2 – b2 – c2 + d2 – 2ad + 2bc}{{a2 – b2 – c2 + d2 + 2ad – 2bc}
= {(a2 – 2ad + d2) – (b2 – 2bc + c2)}(a2 + 2ad + d2) – (b2 + 2bc + c2)}
= {(a – d)2 – (b – c)2}{(a + d)2 – (b + c)2}
= {(a – d) – (b – c)} {(a – d) + (b – c)}{(a + d) – (b + c)} {(a + d) + (b + c)}
= (a – d – b + c)(a – d + b – c)(a + d – b – c)(a + d + b + c)
= (a+b+c+d)(a-b-c+d) (a+b –c-d)(a-b+c-d)
(xxviii) 3x2 – y2 + z2 – 2xy – 4xz
= 4x2 – x2 – y2 + z2 – 2xy – 4xz
= 4x2 – 4xz + z2 – (x2 + 2xy + y2)
= {(2x)2 – 2.2x.z + (z)2} – (x + y)2
= (2x – z)2 – (x + y)2
= {(2x – z) – (x + y)} {(2x – z) + (x + y)}
= (2x – z – x – y)(2x – z + x + y)
= (x – y – z) (3x + y – z)
2) উৎপাদকে বিশ্লেষণ করি –
(i) 81x4 + 4y4
= (9x2)2 + (2y2)2
= (9x2 + 2y2)2 – 2 . 9x2 . 2y2
= (9x2 + 2y2)2 – 36x2y2
= (9x2 + 2y2)2 – (6xy)2
= (9x2 + 2y2 – 6xy) (9x2 + 2y2 + 6xy)
(ii) p4 – 13p2q2 + 4q4
= p4 + 4q4 – 13p2q2
= (p2)2 + (2q2)2 – 13p2q2
= (p2 – 2q2)2 + 2 . p2 . 2q2 – 13p2q2
= (p2 – 2q2)2 + 4p2q2 – 13p2q2
= (p2 – 2q2)2 – 9p2q2
= (p2 – 2q2)2 – (3pq)2
= (p2 – 2q2 + 3pq) (p2 – 2q2 – 3pq)
(iii) x8 – 16y8
= (x4)2 – (4y4)2
= (x4 – 4y4)(x4 + 4y4)
= {(x2)2 – (2y2)2} {(x2 )2+ (2y2) 2}
= (x2 – 2y2)(x2 + 2y2){(x2 + 2y2)2 -2. x2. 2y2 }
= (x2 – 2y2)(x2 + 2y2) {(x2+2y2)2 – 4x2y2}
= (x2 – 2y2)(x2 + 2y2) {(x2+2y2)2 – (2xy)2}
= (x2 – 2y2) (x2 + 2y2) (x2+2y2 +2xy) (x2+2y2-2xy)
= (x2+2xy+2y2) (x2-2xy+ 2y2) (x2+2y2) (x2 -2y2)
(iv) x4 + x2y2 + y4
= (x2)2 + (y2)2 + x2y2
= (x2 + y2)2 – 2x2y2 + x2y2
= (x2 + y2)2 – x2y2
= (x2 + y2)2 – (xy)2
= (x2 + y2 – xy)(x2 + y2 + xy)
(v) 3x4 + 2x2y2 – y4
= 4x4 – x4 + 2x2y2 – y4
= (2x2)2 – (x4 – 2x2y2 + y4)
= (2x2)2 – {(x2)2 – 2x2y2 + (y2)2}
= (2x2)2 – (x2 – y2)2
= {2x2 – (x2 – y2)} {2x2 + (x2 – y2)}
= (2x2 – x2 + y2)(2x2 + x2 – y2)
= (x2 + y2)(3x2 – y2)
(vi) x4 + x2 + 1
(vii) x4 + 6x2y2 + 8y4
(viii) 3x2 – y2 + z2 – 2xy – 4xz
(ix) 3x4 – 4x2y2 + y4
(x) p4 – 2p2q2 – 15q4
(xi) x8 + x4y4 + y8