Class 7 Math BD-সপ্তম শ্রেণি সাধারণ গণিতঃ অনুশীলনী-৫.৩ উৎপাদকে বিশ্লেষন
Class 7 Math book solution BD pdf,Math lecture guide for class 7,class 7 math bd pdf,গণিত সপ্তম শ্রেণি অনুশীলনী-৫.৩ উৎপাদকে বিশ্লেষন
27 January
উৎপাদকে বিশ্লেষন
উৎপাদকে
বিশ্লেষণ করঃ
১. x2+xy+zx+yz
সমাধানঃ
২. a2+bc+ca+ab
সমাধানঃ
a2+bc+ca+ab
=a(a+b)+c(a+b)
=(a+b)(a+c)
=a(a+b)+c(a+b)
=(a+b)(a+c)
৩. ab(px+qy)+a2qx+b2py
সমাধানঃ
ab(px+qy)+a2qx+b2py
= abpx+abqy+a2qx+b2py
= a2qx+ abpx+ abqy+ b2py
=ax(aq+bp)+by(aq+bp)
=(aq+bp)(ax+by)
= abpx+abqy+a2qx+b2py
= a2qx+ abpx+ abqy+ b2py
=ax(aq+bp)+by(aq+bp)
=(aq+bp)(ax+by)
৪. 4x2-y2
সমাধানঃ
4x2-y2
=(2x)2-y2
=(2x+y)(2x-y)
=(2x)2-y2
=(2x+y)(2x-y)
৫. 9a2-4b2
সমাধানঃ
9a2-4b2
=(3a)2-(2b)2
=(3a+2b)(3a-2b)
=(3a)2-(2b)2
=(3a+2b)(3a-2b)
৬. a2b2-49y2
সমাধানঃ
a2b2-49y2
= (ab)2-(7y)2
=(ab-7y)(ab+7y)
= (ab)2-(7y)2
=(ab-7y)(ab+7y)
৭. 16x4-81y4
সমাধানঃ
16x4-81y4
=(4x2-9y2)( 4x2+9y2)
={(2x)2-(3y)2}(4x2+9y2)
=(2x-3y)(2x+3y)( 4x2+9y2)
=(4x2-9y2)( 4x2+9y2)
={(2x)2-(3y)2}(4x2+9y2)
=(2x-3y)(2x+3y)( 4x2+9y2)
৮. a2-(x+y)2
সমাধানঃ
a2-(x+y)2
={a-(x+y)}{a+(x+y)}
=(a-x-y)(a+x+y)
={a-(x+y)}{a+(x+y)}
=(a-x-y)(a+x+y)
৯. (2x-3y+5z)2-(x-2y+3z)2
সমাধানঃ
(2x-3y+5z)2-(x-2y+3z)2
={2x-3y+5z-(x-2y+3z)}{ 2x-3y+5z+(x-2y+3z)}
=(2x-3y+5z-x+2y-3z)(2x-3y+5z+x-2y+3z)
=(x-y+2z)(3x-5y+8z)
={2x-3y+5z-(x-2y+3z)}{ 2x-3y+5z+(x-2y+3z)}
=(2x-3y+5z-x+2y-3z)(2x-3y+5z+x-2y+3z)
=(x-y+2z)(3x-5y+8z)
১০. 4+8a2+9a4
সমাধানঃ
4+8a2+9a4
=(2)2+2*2*3a2+(3a2)2-4a2
=(2+3a2-2a)(2+3a2+2a)
=(2)2+2*2*3a2+(3a2)2-4a2
=(2+3a2-2a)(2+3a2+2a)
১১. 2a2+6a-80
সমাধানঃ
2a2+6a-80
=2(a2+3a-40)
=2(a2+8a-5a-40)
=2{a(a+8)-5(a+8)}
=2(a+8)(a-55)
=2(a2+3a-40)
=2(a2+8a-5a-40)
=2{a(a+8)-5(a+8)}
=2(a+8)(a-55)
১২. y2-6y-91
সমাধানঃ
y2-6y-91
= y2-13y+7y-91
= y(y-13)+7(y-13)
=(y+7)(y-13)
= y2-13y+7y-91
= y(y-13)+7(y-13)
=(y+7)(y-13)
১৩. p2-15p+56
সমাধানঃ
p2-15p+56
= p2-7p-8p+56
=p(p-7)-8(p-7)
=(p-7)(p-8)
= p2-7p-8p+56
=p(p-7)-8(p-7)
=(p-7)(p-8)
১৪. 45a8-5a4x4
সমাধানঃ
45a8-5a4x4
=5a4(9a4-x4)
=5a4{(3a2)2-(x2)2}
=5a4(3a2+x2)( 3a2-x2)
=5a4(9a4-x4)
=5a4{(3a2)2-(x2)2}
=5a4(3a2+x2)( 3a2-x2)
১৫. a2+3a-40
সমাধানঃ
a2+3a-40
= a2+8a-5a-40
=a(a+8)-5(a+8)
=(a-5)(a+8)
= a2+8a-5a-40
=a(a+8)-5(a+8)
=(a-5)(a+8)
১৬. (x2+1)2-(y2+1)2
সমাধানঃ
(x2+1)2-(y2+1)2
=(x2+1+y2+1) (x2+1-y2-1)
=(x2+y2+2) (x2-y2)
=(x2+y2+2) (x-y)(x+y)
=(x2+1+y2+1) (x2+1-y2-1)
=(x2+y2+2) (x2-y2)
=(x2+y2+2) (x-y)(x+y)
১৭. x2+11x+30
সমাধানঃ
x2+11x+30
= x2+6x+5x+30
=x(x+6)+5(x+6)
=(x+6)(x+5)
= x2+6x+5x+30
=x(x+6)+5(x+6)
=(x+6)(x+5)
১৮. a2-b2+2bc-c2
সমাধানঃ
a2-b2+2bc-c2
= a2-(b2-2bc+c2)
=a2-(b-c)2
={a-(b-c)}{a+(b-c)}
=(a-b+c)(a+b-c)
= a2-(b2-2bc+c2)
=a2-(b-c)2
={a-(b-c)}{a+(b-c)}
=(a-b+c)(a+b-c)
১৯. 144x7-25x3a4
সমাধানঃ
144x7-25x3a4
=x3(144x4-25a4)
= x3{(12x2)2-(5a2)2}
=x3(12x2+5a2)(12x2-5a2)
=x3(144x4-25a4)
= x3{(12x2)2-(5a2)2}
=x3(12x2+5a2)(12x2-5a2)
২০. 4x2+12xy+9y2-16a2
সমাধানঃ
4x2+12xy+9y2-16a2
=(2x)2+2*2x*3y+(3y)2-(4a)2
=(2x+3y)2-(4a)2
=(2x+3y-4a)(2x+3y+4a)
=(2x)2+2*2x*3y+(3y)2-(4a)2
=(2x+3y)2-(4a)2
=(2x+3y-4a)(2x+3y+4a)