ক্লাস ৯ কষে দেখি ৮.৫ সমাধান | কষে দেখি ৮.৫ | Koshe Dekhi 8.5 | Class 9 Koshe Dekhi 8.5 Solution. Get the solution of Koshe dekhi 8.5 Class 9. Here we will provide the solutions of Chapter 8 Part 5 of WBBSE Class 9 Maths.
Koshe Dekhi 8.5 Class 9 Solution
নীচের বীজগাণিতিক সংখ্যামালাগুলিকে উৎপাদকে বিশ্লেষণ করি।
ক্লাস ৯ কষে দেখি ৮.৫ উৎপাদকে বিশ্লেষণ Question 1 সমাধান: Factorise (a+b)2-5a-5b+6
Ex 1.(i). (a+b)2 –5a –5b +6
সমাধান:
(a+b)2 -5a-5b +6
= (a+b)2 -5(a+b) +6
ধরি, (a+b) = x
∴ প্রদত্ত রাশিমালাটি হল =
x2 -5x +6
= x2 -(2+3)x +6
= x2 -2x -3x +6
= x(x-2) -3(x-2)
= (x-2)(x-3)
= (a+b-2)(a+b-3) [যেহেতু x = a+b] উত্তর
Factorise (x+1)(x+2)(3x-1)(3x-4)+12
Ex 1.(ii). (x+1)(x+2)(3x-1)(3x-4) +12
সমাধান:
(x+1)(x+2)(3x-1)(3x-4) +12
= {(x+1)(3x-1)} {(x+2)(3x-4)} +12
= (3x2 +3x -x -1)(3x2 +6x-4x -8) +12
= (3x2+2x -1)(3x2+2x -8)+12
[ধরি, 3x2+2x = a]
= (a-1)(a-8) +12
= a2 -a-8a +8+12
=a2 -9a +20
= a2 -(4+5)a +20
= a2 -4a -5a +20
= a(a-4)-5(a-4)
= (a-4) (a-5)
= (3x2+2x-4)(3x2+2x-5) [যেহেতু a = x2+2x]
= (3x2 +2x-4) {3x2 +(5-3)x -5 }
= (3x2+2x-4) (3x2 +5x -3x -5)
= (3x2+2x-4) {x(3x+5) -1(3x+5)}
= (3x2+2x-4) (3x+5)(x-1)
= (x-1)(3x+5)(3x2+2x-4) উত্তর
Factorise x(x2-1)(x+2)-8
Ex 1.(iii). x(x2-1)(x+2) -8
সমাধান:
x(x2-1)(x+2)-8
= x(x+1)(x-1)(x+2) -8
= {x(x+1)} {(x-1)(x+2)} -8
= (x2+x) (x2-x+2x-2) -8
= (x2+x) (x2+x-2) -8
[ধরি, x2+x = a]
= a(a-2) -8
= a2-2a -8
= a2-(4-2)a -8
= a2 -4a +2a -8
= a(a-4) +2(a-4)
= (a-4)(a+2)
= (x2+x -4)(x2+x+2) [যেহেতু a = x2+x] উত্তর
Ex 1.(iv). 7(a2+b2) -15(a4-b4) +8(a2-b2)2
সমাধান:
7(a2+b2) -15(a4-b4) +8(a2-b2)2
= 7(a2+b2) -15(a2+b2)(a2-b2) +8(a2-b2)2
[ধরি, a2+b2 = x এবং a2-b2 = y]
= 7x2 -15xy + 8y2
= 7x2 -(7+8)xy +8y2
= 7x2 -7xy – 8xy +8y2
= 7x(x-y) -8y(x-y)
= (x-y)(7x-8y)
= {(a2+b2) – (a2-b2)} {7(a2+b2) – 8(a2 – b2)} [x ও y –এর মান বসিয়ে পাই]
= 2b2(15b2 -a2) উত্তর
Ex 1.(v). (x2-1)2 +8x(x2+1) +19x2
সমাধান:
(x2-1)2+8x(x2+1) +19x2
= (x2 +1)2 -4x2 +8x(x2+1) +19x2 যেহেতু (x2-1)2 = (x2 +1)2 -4x2
= (x2+1)2 +8x(x2+1) +15x2
[ধরি, x2+1 = a]
= a2 +8ax +15x2
= a2 +(3+5)ax +15x2
= a2 +3ax +5ax +15x2
= a(a +3x) +5x(a +3x)
= (a +3x)(a +5x)
= (x2+1+3x)(x2+1+5x) [যেহেতু a = x2+1]
= (x2+3x+1)(x2+5x+1) উত্তর
Ex 1.(vi). (a-1)x2 -x -(a-2)
সমাধান:
(a-1)x2 –x-(a-2)
= (a-1)x2 -(a-1 -a+2)x -(a-2)
= (a-1)x2 -{(a-1) -(a-2)}x -(a-2)
= (a-1)x2 -(a-1)x +(a-2)x -(a-2)
= (a-1)(x2 -x) +(a-2)(x-1)
= (a-1)x(x-1) +(a-2)(x-1)
= (x-1) {x(a-1)+(a-2)}
= (x-1) (ax-x+a-2) উত্তর
Ex 1.(vii). (a-1)x2 +a2xy +(a+1)y2
সমাধান:
(a-1)x2 +a2xy +(a+1)y2
= (a-1)x2 +(a2-1+1)xy +(a+1)y2
= (a-1)x2 +{(a+1)(a-1) +1}xy +(a+1)y2
= (a-1)x2 +(a+1)(a-1)xy +xy +(a+1)y2
= (a-1)x {x+(a+1)y} +y{x+(a+1)y}
= {x+(a+1)y}{(a-1)x+y}
= (x+ay+y)(ax -x+y) উত্তর
Ex 1.(viii). x2 -qx -p2 +5pq -6q2
সমাধান:
Ex 1.(ix). 2(a2+$\frac{1}{a^2}$) -(a-$\frac{1}{a}$)-7
সমাধান:
Ex 1.(x). (x2-x)y2 +y -(x2+x)
সমাধান:
(x2-x)y2 +y -(x2+x)
= x(x-1)y2 +y -x(x+1)
= x(x-1)y2 +{x2-(x2 -1)}y -x(x+1)
= x(x-1)y2 +{x2-(x+1)(x-1)}y -x(x+1)
= x(x-1)y2 + x2y -(x+1)(x-1)y -x(x+1)
= xy{(x-1)y+x} – (x+1){(x- 1)y+x}
= xy(xy-y+x) – (x+1)(xy-y+x)
= (xy -y +x)(xy -x -1) উত্তর