Toán Lớp 8: Rút gọn a, (3x+5) ²+(3x-5) ²-(3x+2)(3x-2) b,2(x-y)(x+y)+(x+y) ²+(x-y) ² c,(x-y+z) ²+(z-y) ²+2(x-y+z)(y-z)

Question

Toán Lớp 8:  Rút gọn a, (3x+5) ²+(3x-5) ²-(3x+2)(3x-2) b,2(x-y)(x+y)+(x+y) ²+(x-y) ² c,(x-y+z) ²+(z-y) ²+2(x-y+z)(y-z)

cobebongdem · Answer

(3x+5)&sup2;+(3x-5)&sup2;-(3x+2)(3x-2)   =9x&sup2;+30x+25+9x&sup2;-30x+25-9x&sup2;+4   =9x&sup2;+54   ............   2(x-y)(x+y)+(x+y)&sup2;+(x-y)&sup2;   =(x-y)&sup2;+2(x-y)(x+y)+(x+y)&sup2;   =(x-y+x+y)&sup2;   =4x&sup2;   ........   (x-y+z)&sup2;+(z-y)&sup2;+2(x-y+z)(y-z)   =(z-y)&sup2;-2(z-y)(x-y+z)+(x-y+z)&sup2;   =(z-y-x+y-z)&sup2;   =(-x)&sup2;   =x&sup2;

truongthanhhung · Answer

Giải đáp:   a)9x&sup2;+54   b)4x&sup2;   c)x&sup2;   Lời giải và giải thích chi tiết:   a)(3x+5)&sup2;+(3x-5)&sup2;-(3x+2)(3x-2)   =(3x)&sup2;+2.3x.5+5&sup2;+(3x)&sup2;-2.3x.5+5&sup2;-[(3x)&sup2;-2&sup2;]   =9x&sup2;+30x+25+9x&sup2;-30x+25-(9x&sup2;-4)   = 9x&sup2;+30x+25+9x&sup2;-30x+25-9x&sup2;+4   =(9x&sup2;+9x&sup2;-9x&sup2;)+(30x-30x)+(25+25+4)   =9x&sup2;+54   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;                          (A-B)&sup2;=A&sup2;-2AB+B&sup2;                          A&sup2;-B&sup2;=(A+B)(A-B)   b)2(x-y)(x+y)+(x+y)&sup2;+(x-y)&sup2;   =(x-y)&sup2;+2(x-y)(x+y)+(x+y)&sup2;   =(x-y+x+y)^2   =(2x)^2   =4x&sup2;   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;   c)(x-y+z)&sup2;+(z-y)&sup2;+2(x-y+z)(y-z)   =(x-y+z)&sup2;+2(x-y+z)(y-z)+(y-z)&sup2;   =(x-y+z+y-z)&sup2;   =x&sup2;   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;