Question

(x+y)^3+(x-y)^3=?

Answer 1

(*) (x+y)³=(x+y)(x+y)(x+y)

=(x+y).[x(x+y)+y(x+y)]

=(x+y).(x²+xy+xy+y²)

=(x+y).(x²+2xy+y²)

=x(x²+2xy+y²)+y(x²+2xy+y²)

=x³+2x²y+xy²+x²y+2xy²+y³

=x³+(2x²y+x²y)+(xy²+2xy²)+y³=x³+3x²y+3xy² (1)

(*)(x-y)³=(x-y)(x-y)(x-y)

=(x-y).[x(x-y)-y(x-y)]

=(x-y).(x²-xy-xy+y²)

=(x-y).(x²-2xy+y²)

=x(x²-2xy+y²)-y(x²-2xy+y²)

=x³-2x²y+xy²-x²y+2xy²-y³

=x³+(-2x²-x²y)+(xy²+2xy²)-y³=x³-3x²y+3xy²-y³ (2)

Từ (1);(2)=>(x+y)³+(x-y)³=x³+3x²y+3xy²+y³+x³-3x²y+3xy²-y³=2x³+6xy²

Answer 2

giải kiểu này mỏi tay quá,thôi bn ghi nhớ 2 hằng đẳng thức này nhé:(sau này áp dụng để giaỉ các bài tương tự)

1,(x+y)³=x³+3x²y+3xy²+y³

2,(x-y)³=x³-3x²y+3xy²-y³

Answer 3

(x+y)³=(x+y)(x+y)(x+y)

=(x+y).[x(x+y)+y(x+y)]

=(x+y).(x²+xy+xy+y²)

=(x+y).(x²+2xy+y²)

=x(x²+2xy+y²)+y(x²+2xy+y²)

=x³+2x²y+xy²+x²y+2xy²+y³

=x³+(2x²y+x²y)+(xy²+2xy²)+y³=x³+3x²y+3xy² (1)

(x-y)³=(x-y)(x-y)(x-y)

=(x-y).[x(x-y)-y(x-y)]

=(x-y).(x²-xy-xy+y²)

=(x-y).(x²-2xy+y²)

=x(x²-2xy+y²)-y(x²-2xy+y²)

=x³-2x²y+xy²-x²y+2xy²-y³

=x³+(-2x²-x²y)+(xy²+2xy²)-y³=x³-3x²y+3xy²-y³ (2)

Từ (1);(2)=>(x+y)³+(x-y)³=x³+3x²y+3xy²+y³+x³-3x²y+3xy²-y³=2x³+6xy²

Answer 4

(*) (x+y)³=(x+y)(x+y)(x+y)

=(x+y).[x(x+y)+y(x+y)]

=(x+y).(x²+xy+xy+y²)

=(x+y).(x²+2xy+y²)

=x(x²+2xy+y²)+y(x²+2xy+y²)

=x³+2x²y+xy²+x²y+2xy²+y³

=x³+(2x²y+x²y)+(xy²+2xy²)+y³=x³+3x²y+3xy² (1)

(*)(x-y)³=(x-y)(x-y)(x-y)

=(x-y).[x(x-y)-y(x-y)]

=(x-y).(x²-xy-xy+y²)

=(x-y).(x²-2xy+y²)

=x(x²-2xy+y²)-y(x²-2xy+y²)

=x³-2x²y+xy²-x²y+2xy²-y³

=x³+(-2x²-x²y)+(xy²+2xy²)-y³=x³-3x²y+3xy²-y³ (2)

Từ (1);(2)=>(x+y)³+(x-y)³=x³+3x²y+3xy²+y³+x³-3x²y+3xy²-y³=2x³+6xy²

Answer 5

(*) (x+y)³=(x+y)(x+y)(x+y)

=(x+y).[x(x+y)+y(x+y)]

=(x+y).(x²+xy+xy+y²)

=(x+y).(x²+2xy+y²)

=x(x²+2xy+y²)+y(x²+2xy+y²)

=x³+2x²y+xy²+x²y+2xy²+y³

=x³+(2x²y+x²y)+(xy²+2xy²)+y³=x³+3x²y+3xy² (1)

(*)(x-y)³=(x-y)(x-y)(x-y)

=(x-y).[x(x-y)-y(x-y)]

=(x-y).(x²-xy-xy+y²)

=(x-y).(x²-2xy+y²)

=x(x²-2xy+y²)-y(x²-2xy+y²)

=x³-2x²y+xy²-x²y+2xy²-y³

=x³+(-2x²-x²y)+(xy²+2xy²)-y³=x³-3x²y+3xy²-y³ (2)

Từ (1);(2)=>(x+y)³+(x-y)³=x³+3x²y+3xy²+y³+x³-3x²y+3xy²-y³=2x³+6xy²