lx rùi bạn. Đăng lại nhé

\(S=1+3+7+16+...+1023\)

\(1+1+1=3\)

\(3\cdot2+1=7\)

\(7\cdot2+1=15.\)

\(15\cdot2+1=31\)

\(31\cdot2+1=63\)

\(63\cdot2+1=127\)

\(127\cdot2+1=255\)

\(255\cdot2+1=511\)

\(511\cdot2+1=1023\)

\(Ta\) \(cộng\) \(tất\) \(cả\) \(với\) \(nhau:\)

\(S=2036.\)

\(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)

\(=x^4-3x^3y+3x^2y^2-xy^3-y^3+2xy^2-x^2y-xy^2+y^3\)

\(=x^4-xy^3-x^2y+xy^2-3x^3y+3x^2y^2\)

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

lx tùi bẹn

\(a.\left(x+2\right)\left(x^2-2x+4\right)=x\left(x^2-2x+4\right)+2\left(x^2-2x+4\right)\)

\(=x^3-2x^2+4x+2x^2-4x+8=x^3+8.\)

\(b.\left(x+2y+z\right)\left(x-2x-z\right)\)

\(=x\left(x-2x-z\right)+2y\left(x-2x-z\right)+z\left(x-2x-z\right)\)

\(=-x^2-xz-2xy-2yz-xz-z^2=-2xy-2yz-x^2-2xz-z^2.\)

\(c.\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x\left(x^2+3xy+9y^2\right)-3y\left(x^2+3xy+9y^2\right)\)

\(=x^3+3x^2y+9xy^2-3x^2y-9xy^2-27y^3=x^3-27y^3.\)

\(d.\left(x^2-3\right)\left(x^4+3x^2+9\right)=x^2\left(x^4+3x^2+9\right)-3\left(x^4+3x^2+9\right)\)

\(=x^6+3x^4+9x^2-3x^4-9x^2-27=x^6-27.\)

\(e.\left(5+3x\right)^3=5^3+3\cdot5^2\cdot3x+3\cdot5\cdot\left(3x\right)^2+\left(3x\right)^2\)

\(=125+225x+135x^2+27x^3.\)

\(g.\left(2x-1\right)\left(4x^2+2x+1\right)=2x\left(4x^2+2x+1\right)-1\left(4x^2+2x+1\right)\)

\(=8x^3+4x^2+2x-4x^2-2x-1=8x^3-1.\)