Toán Lớp 8: a) x^2-y^2-2x+2y b) x^2-x-6 c) (x+y+z)^3-x^3-y^3-z^3

Question

Toán Lớp 8:  a) x^2-y^2-2x+2y b) x^2-x-6 c) (x+y+z)^3-x^3-y^3-z^3

minhhaanh · Answer

$a,x^2-y^2-2x+2y  =(x-y)(x+y) - 2 (x-y)  =(x-y)(x+y-2)  b, x^2-x-6  =x^2+2x-3x-6  =x(x+2)-3(x+2)  =(x+2)(x-3)  c, (x+y+z)^3-x^3-y^3-z^3  =[(x+y)+z]^3-x^3-y^3-z^3  =(x+y)^3 +z^3 + 3 (x+y)z(x+y+z) -x^3-y^3-z^3  =x^3 + y^3+z^3 + 3xy(x+y)+3(x+y)z(x+y+z)-x^3-y^3-z^3  =3(x+y) (xy + xz + yz +z^2)  =3(x+y) [x(y+z) + z (y+z)]  =3(x+y)(x+z)(y+z)$

hongocha12 · Answer

Giải đáp+Lời giải và giải thích chi tiết:   a)x&sup2;-y&sup2;-2x+2y   =(x&sup2;-y&sup2;)-(2x-2y)   =(x-y)(x+y)-2(x-y)   =(x-y)(x+y-2)   b)x&sup2;-x-6   =x&sup2;-3x+2x-6   =x(x-3)+2(x-3)   =(x-3)(x+2)   **c)(x+y+z)&sup3;-x&sup3;-y&sup3;-z&sup3;   =[(x+y+z)&sup3;-x&sup3;]-(y&sup3;+z&sup3;)   =(x+y-z+x)[(x+y+z)&sup2;+(x+y+z)x+x&sup2;]-(y+z)(y&sup2;-yz+z&sup2;)   =3(y+z)(x&sup2;+xy+xz+yz)