Question

Rút gọn biểu thức sau:

a) (x+y)\(^{3^{ }}\)-3xy.(x+y)

b) (x-2)\(^3\)-x\(^2\).(x-6)-7

c) (a+b)\(^2\)-(a-b)\(^2\)-4ab

Answer 1

a)\(\left(x+y\right)^3-3xy\left(x+y\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^2-3xy\right]\)

\(=\left(x+y\right)\left[x^2+2xy+y^2-3xy\right]\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)=x^3+y^3\)

b)\(\left(x-2\right)^3-x^2\left(x-6\right)-7\)

\(=x^3-6x^2+12x-8-x^3+6x^2-7\)

\(=12x-15\)

c)\(\left(a+b\right)^2-\left(a-b\right)^2-4ab\)

\(=a^2+2ab+b^2-a^2+2ab-b^2-4ab\)

\(=0\)