Toán Lớp 8: phân tích đa thức thành nhân tử dùng phương pháp bổ sung hằng đẳng thức x^2-4x+5 x^2-9x+20 9x^2-6x-3 x^2-xy-6y^2

Question

Toán Lớp 8:  phân tích đa thức thành nhân tử dùng phương pháp bổ sung hằng đẳng thức x^2-4x+5 x^2-9x+20 9x^2-6x-3 x^2-xy-6y^2

hatuanlan · Answer

x^2-4x-5   =x^2-2.2.x+4-9   =(x-2)^2-9   =(x-2-3)(x-2+3)   =(x-5)(x+1)   x^2-9x+20   =x^2-2.x. 9/2 +(81)/4-1/4   =(x-9/2)^2-1/4   =(x-9/2-1/2)(x-9/2+1/2)   =(x-5)(x-4)   9x^2-6x-3   =9x^2-2.3x.1+1-4   =(3x-1)^2-4   =(3x-1-2)(3x-1+2)   =(3x-3)(3x+1)   x^2-xy-6y^2   =x^2-4y^2-2y^2-xy   =(x-2y)(x+2y)-y(x+2y)   =(x+2y)(x-2y-y)   =(x+2y)(x-3y)

chauhoangmy98 · Answer

a)   Sửa đề:x&sup2;-4x+5   &rarr;x&sup2;-4x-5    C&aacute;ch 1:    x&sup2;-4x-5   =x&sup2;-5x+x-5   =(x&sup2;-5x)+(x-5)   =x(x-5)+(x-5)   =(x-5)(x+1)    C&aacute;ch 2:    x&sup2;-4x-5   =x&sup2;-4x+4-9   =(x&sup2;-4x+4)-9   =(x&sup2;-2.x.2+2&sup2;)-9   =(x-2)&sup2;-3&sup2;   =(x-2+3)(x-2-3)   =(x+1)(x-5)   b)    C&aacute;ch 1:    x&sup2;-9x+20   =x&sup2;-5x-4x+20   =(x&sup2;-5x)-(4x-20)   =x(x-5)-4(x-5)   =(x-5)(x-4)    C&aacute;ch 2:    x&sup2;-9x+20   =x&sup2;-9x+81/4-1/4   =(x&sup2;-9x+81/4)-1/4   =[x&sup2;-2.x. 9/2+(9/2)^2]-1/4   =(x-9/2)^2-(1/2)^2   =(x-9/2+1/2)(x-9/2-1/2)   =(x-8/2)(x-10/2)   =(x-4)(x-5)   c)    C&aacute;ch 1:    9x&sup2;-6x-3   =3(3x&sup2;-2x-1)   =3(3x&sup2;-3x+x-1)   =3[(3x&sup2;-3x)+(x-1)]   =3[3x(x-1)+(x-1)]   =3(x-1)(3x+1)    C&aacute;ch 2:    9x&sup2;-6x-3   =9x&sup2;-6x+1-4   =(9x&sup2;-6x+1)-4   =[(3x)&sup2;-2.3x.1+1&sup2;]-4   =(3x-1)&sup2;-2&sup2;   =(3x-1+2)(3x-1-2)   =(3x+1)(3x-3)   =3(3x+1)(x-1)   d)    C&aacute;ch 1:    x&sup2;-xy-6y&sup2;   =x&sup2;-3xy+2xy-6y&sup2;   =(x&sup2;-3xy)+(2xy-6y&sup2;)   =x(x-3y)+2y(x-3y)   =(x-3y)(x+2y)    C&aacute;ch 2:    x&sup2;-xy-6y&sup2;   =x&sup2;-xy+1/4y&sup2;-25/4y&sup2;   =(x&sup2;-xy+1/4y&sup2;)-25/4y&sup2;   =[x&sup2;-2.x. 1/2y+(1/2y)^2]-25/4y&sup2;   =(x-1/2y)^2-(5/2y)^2   =(x-1/2y+5/2y)(x-1/2y-5/2y)   =(x+4/2y)(x-6/2y)   =(x+2y)(x-3y)