Toán Lớp 8: b) (a^2 + b^2)(x^2 + y^2) = (ax – by)^2 + (bx + ay)^2 c) a^3 – b^3 + ab(a – b) = (a – b)(a + b)^2

Question

Toán Lớp 8:  b) (a^2 + b^2)(x^2 + y^2) = (ax – by)^2 + (bx + ay)^2   c) a^3 – b^3 + ab(a – b) = (a – b)(a + b)^2

maingoctruc · Answer

a) (ax-by)^2+(bx+ay)^2   =a^2x^2-2abxy+b^2y^2+b^2x^2+2abxy+a^2y^2   =a^2x^2+b^2y^2+b^2x^2+a^2y^2   =a^2(x^2+y^2)+b^2(x^2+y^2)   =(x^2+y^2)(a^2+b^2) ( text{đpcm})   b) a^3-b^3+ab(a-b)   =(a-b)(a^2+ab+b^2)+ab(a-b)   =(a-b)(a^2+ab+b^2+ab)   =(a-b)(a^2+2ab+b^2)   =(a-b)(a+b)^2 ( text{đpcm})

thucquyenlan · Answer

b)VT=(a&sup2;+b&sup2;)(x&sup2;+y&sup2;)             =a&sup2;x&sup2;+a&sup2;y&sup2;+b&sup2;x&sup2;+b&sup2;y&sup2;             =a&sup2;x&sup2;+a&sup2;y&sup2;+b&sup2;x&sup2;+b&sup2;y&sup2;+2abxy-2abxy             =(a&sup2;x&sup2;-2abxy+b&sup2;y&sup2;)+(b&sup2;x&sup2;+2abxy+a&sup2;y&sup2;)             =[(ax)&sup2;-2.ax.by+(by)&sup2;]+[(bx)&sup2;+2.bx.ay+(ay)&sup2;]             =(ax-by)&sup2;+(bx+ay)&sup2;             =VP   &rArr;đpcm   c)VT=a&sup3;-b&sup3;+ab(a-b)             =(a-b)(a&sup2;+ab+b&sup2;)+ab(a-b)             =(a-b)(a&sup2;+ab+b&sup2;+ab)             =(a-b)(a&sup2;+2ab+b&sup2;)             =(a-b)(a+b)&sup2;             =VP   &rArr;đpcm