নবম শ্রেণীর গণিত কষেদেখি 8.2 সমাধান /class 9 math 9.2 chapter solution
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নবম শ্রেণীর
গণিত
কযে দেখি – 8.2
x⁴ y⁴
1. -------- – -----
16 81
x y
= (------)²– (-----)²
4 9
x² y² x² y²
= (------+ ------) ( --- - ----)
4 9 4 9
x² y² x² y²
= (-------+ ------) ( ------- )-( ----)
4 9 2 3
[a² – b²-এর মান নির্নায়ক সূত্র ব্যবহার ]
x² y² x y x y
= (-------+ ------) ( --- - -----)( ------- + -----)
4 9 2 3 2 3
1 2
2. m +---- + 2 - 2m - ----
m m
1 1 1
= m² + 2 × m × ---- -- + ----–-- - 2/(m+-----)
m m² m
1 1
=(m+-----)² - 2(m+-------)
m m
1 1
=(m+-----) (m+------ -2)(Ans)
m m
3. 9qp²-24pq + 16q²+3ap-4aq
= (3p)² - 2x. 3p. 4q+(4g)²+ a (3p-4q)
= (3p-4q)²+a (3p-4g)
= (3p-4q) (3p-4q+a)
4. 4x⁴+81
= (2x²)²+9²+2 x 2x²× 9-36x²
= (2x² + 9)²-(6x)²
= (2x² + 9 + 6x) (2x²+9-6x)
= (2x²+6x + 9) (2x² - 6x +9
5.x⁴ - 7x²+1
(x²)² + 1²+2 × x²×1-9x²
= (x²+ 1)²-(3x)²
= (x²+ 1-3x) (x²+1 + 3x)
= (x²+ 1-3x) (x²+1 + 3x)
= (x²-3x + 1) (x² + 3x + 1)
6. p-11p²q²+q
= (p²)²-2p²q² + (q²)²-9p²q²
=(p²-q²)²-(3gp)²
=(p²-q²-3pq) (p²-q² + 3pq)
=(p²-3pq-q²) (p²+3pq-q²)
7. a²+b²-c²-2ab
= (a²-2ab+b²)-c²
= (a-b)²-c².
= (a-b-c) (a-b+c)
8. 3a (3a+2c)-4b (b + c)
=9a²+6ac-4b²-4bc
= (9a²-4b²)+2c (3a-2b)
= (3a-2b) (3a+2b) + 2c (3a-2b)
= (3a-2b) (3a + 2b +2c)
9. a²-6ab + 12bc-4c²
= a²4c²-6b(a-2c)
= (a-2c) (a +2c)-6b (a-2c)
=(a-2c) (a +2c-6b)
= (a-2c) (a-6b+2b)
10. 3a²+4ab+b²-2ac-c²
= (4a²+ 4ab + b²)-a²-2bc-c²
=(2a + b)²(a²+2ac + c²)
=(2a + b)²(a + c)²
= (2a+b+a+c) (2a+b-a-c)
= (3a+b+c) (a+b-c)
11. x²-y²-6ax + 2ay + 8a²
= (x²-6ax +9a²)-(y²-2ay + a²)
= (x-3a)²-(y-a)²
=(x-3a-y+ a) (x-3a+y-a)
=(x-y-2a) (x+y-4b)
.12. a²-9b²+ 4c²-25d²-4ac + 30bd.
= (a²-4ac +4c²)-(9b²-30bd+25d²)
=(a-2c)²-(3b-5d)²
= (a-2c-3b+5d) (a-2c+3b-5d)
= (a-3b-2c+5d) (a + 3b-2c-5d)
14. x²-2x-22499
= (x²-2x + 1)-22500
=(x-1)²-(150)²
=(x-1-150) (x - 1+150)
=(x-151) (x + 149)
15. x² - y²(a²-b²) + 4abxy
= x²a²-x²b²-a²y² + b²y²+4abxy
={(xa)²+ 2abxy + (by)²}-{(ab)²-2abxy+ (ay)²
=(xa+by)²-(xb-ay)²
=(xa + by-xb+ ay) (xa + xy + xb-ay)