Lời giải:
Ta có:
\(x^4+4x^3y+6x^2y^2+4xy^3+y^4-x-y-10\)
\(=(x^4+x^3y)+3(x^3y+2x^2y^2+xy^3)+(xy^3+y^4)-(x+y)-10\)
\(=x^3(x+y)+3xy(x^2+2xy+y^2)+y^3(x+y)-(x+y)-10\)
\(=x^3(x+y)+3xy[x(x+y)+y(x+y)]+y^3(x+y)-(x+y)-10\)
\(=x^3(x+y)+3xy(x+y)^2+y^3(x+y)-(x+y)-10\)
\(=2x^3+6xy(x+y)+2y^3-2-10\)
\(=2[x^3+3xy(x+y)+y^3]-12\)
\(=2[x^2(x+y)+y^2(x+y)+2xy(x+y)]-12\)
\(=2(x+y)(x^2+y^2+2xy)-12=2(x+y)(x+y)^2-12\)
\(=2(x+y)^3-12=2.2^3-12=4\)
Nếu bạn đã biết hằng đẳng thức thì:
\(x^4+4x^3y+6x^2y^2+4xy^3+y^4-x-y-10\)
\(=(x+y)^4-(x+y)-10=2^4-2-10=4\)
=(x4+x3y)+3(x3y+2x2y2+xy3)+(xy3+y4)−(x+y)−10
=x3(x+y)+3xy(x2+2xy+y2)+y3(x+y)−(x+y)−10
=x3(x+y)+3xy[x(x+y)+y(x+y)]+y3(x+y)−(x+y)−10
=x3(x+y)+3xy(x+y)2+y3(x+y)−(x+y)−10
=2[x2(x+y)+y2(x+y)+2xy(x+y)]−12
=2(x+y)(x2+y2+2xy)−12=2(x+y)(x+y)2−12
Nếu bạn đã biết hằng đẳng thức thì:
