class 9 math kose dekhi 8.2 /
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- নবম শ্রেণী গণিত কষে দেখি 8.2
কষে দেখি—৪.2
x⁴. y⁴
1. ------ + ----
16. 81
² ²
( x²) (y²)
= (---------) +( --------)
( 4 ) (9)
( x². y²). ( x² y²)
= ( ------ + ----). (-------- +. -----)
(. 4 9. ). ,(. 4. 9 ,)
( x². y²). ( x)² ( y )²
= ( ------ + ----). (----) ,,- (-----)
(. 4 9. ). ,( 2) (. 3 )
( x². y²). ( x y )( x. y )
= ( ------ + ----). (---- - ----)(---.+ ---)
(. 4 9. ). ,( 2 3 ,)( 2. 3)
-
3.3pq² – 24pq + 16q² +3ap –4aq
= (3p)² - 2×3p ×4q+ (4q)² +a (3p - 4q)
= (3p - 4q)² + a (3p - 4q)
= (3p - 4q) (3p - 4q + a)
4. 4x⁴+81
= (2x²)² + 9²+2× 2x² x 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 x x²x1 - 9x²
= (x² + 1)²–(3x)²
= (x²+ 1 - 3x) (x² + 1 + 3x)
= (x² - 3x + 1) (x² + 3x + 1)
6. p⁴ - 11p²q²+q⁴
= (p²)²--2p²q²+ (q²)²- 9p²q²
=(p²- q²)-(3pq)²
= (p²-q²-3pq) (p²-q²+ 3pq)
= (p2-3pq -q²) (p2 + 3pq - q²)
7. a²+b²-c²-2ab
= (a-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)(Ans)
9. a²-6ab + 12bc-4c²
= a²-4c²-6b(a - 2c)
= (a - 2c) (a + 2c) - 6b (a - 2c)
= (a - 2c)(a + 2c - 6b)
= (a - 2c) (a - 6b + 2b)(Ans)
10. 3a² +4ab+b²-2bc-c²
=(4a² + 4ab + b)- (a² - 2bc - c²)
=(2a + b)²–(a + 2ac + c)²
=(2a + b)²-(a + c)²
= (2a + b + a + c) (2a + b-a-c)
= (3a + b + c)(a + b-c) (Ans)
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)(Ans)
12. (a² - 9b²+ 4c² - 25d² - 4ac + 30bd.
= (a² - 4ac + 4c²) - (9b² - 30bd + 25d³)
= (a - 2c)²-(3b - 5d)²
= (a - 2c-3b + 5d) (a - 2c + 3b - 5d)
(a - 3b-2c + 5d) (a + 3b - 2c - 5d)(Ans)
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 (q² - 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).
(Ans)
আগের পর্ব কষে দেখি 8. 1
পরের পর্ব কষে দেখি 8.3
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