Toán Lớp 8: Rút Gọn bảy hàng thức đáng nhớ a)(x+y)^2+(x-y)^2 b)2(x+y)(x-y)+(x-y)^2+(x+y)^2 c)2(x+3)^2-3(x+1/2)^2+(x-4)^2 d) 126y^3+(x-5y)(x^2+5xy+2

Question

Toán Lớp 8:  Rút Gọn bảy hàng thức đáng nhớ a)(x+y)^2+(x-y)^2 b)2(x+y)(x-y)+(x-y)^2+(x+y)^2 c)2(x+3)^2-3(x+1/2)^2+(x-4)^2 d) 126y^3+(x-5y)(x^2+5xy+25y^2)

truongankimtrong · Answer

Giải đáp:   a)2x&sup2;+2y&sup2; b)4x&sup2; c)x+133/4 d)x&sup3;+y&sup3;   Lời giải và giải thích chi tiết:   a)(x+y)&sup2;+(x-y)&sup2;   =x&sup2;+2xy+y&sup2;+x&sup2;-2xy+y&sup2;   =(x&sup2;+x&sup2;)+(2xy-2xy)+(y&sup2;+y&sup2;)   =2x&sup2;+2y&sup2;   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;                          (A-B)&sup2;=A&sup2;-2AB+B&sup2;   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)&sup2;   =(2x)&sup2;   =4x&sup2;   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;   c)2(x+3)&sup2;-3(x+1/2)^2+(x-4)&sup2;   =2(x&sup2;+6x+9)-3(x&sup2;+x+1/4)+x&sup2;-8x+16   =2x&sup2;+12x+18-3x&sup2;-3x-3/4+x&sup2;-8x+16   =(2x&sup2;-3x&sup2;+x&sup2;)+(12x-3x-8x)+(18-3/4+16)   =x+133/4   &Aacute;p dụng HĐT:(A+B)&sup2;=A&sup2;+2AB+B&sup2;                          (A-B)&sup2;=A&sup2;-2AB+B&sup2;   d)126y&sup3;+(x-5y)(x&sup2;+5xy+25y&sup2;)   =126y&sup3;+(x-5y)[x&sup2;+x.5y+(5y)&sup2;]   =126y&sup3;+x&sup3;-(5y)&sup3;   =126y&sup3;+x&sup3;-125y&sup3;   =x&sup3;+(126y&sup3;-125y&sup3;)   =x&sup3;+y&sup3;   &Aacute;p dụng HĐT:A&sup3;-B&sup3;=(A-B)(A&sup2;+AB+B&sup2;)

cattien · Answer

Giải đáp+Lời giải và giải thích chi tiết:    a, (x + y )&sup2; + (x - y )&sup2;   = x&sup2; + 2xy + y&sup2; + x&sup2; - 2xy + y&sup2;   = 2x&sup2; + 2y&sup2;   b, 2(x + y).(x - y) + (x - y)&sup2; + (x + y)&sup2;   = 2.(x&sup2; - y&sup2;) + x&sup2; - 2xy + y&sup2; + x&sup2; + 2xy + y&sup2;   = 2x&sup2; - 2y&sup2; + 2x&sup2; + 2y&sup2;   = 4x&sup2;   c, 2.(x + 3)&sup2; - 3(x + $ dfrac{1}{2}$)&sup2; + ( x - 4)&sup2;   = 2.(x&sup2; + 6x + 9) - 3.(x&sup2; + x + $ dfrac{1}{4}$) + x&sup2; - 8x + 16   = 2x&sup2; + 12x + 18 - 3x&sup2; - 3x - $ dfrac{3}{4}$ + x&sup2; - 8x + 16   = x + $ dfrac{133}{4}$   d,  126y&sup3; + (x- 5y).(x&sup2; + 5xy + 25y&sup2;)   =  126y&sup3; + x&sup3; - 125y&sup3;   = x&sup3; + y&sup3;