Bài 6:
1: \(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)
2: \(x^3+8y^3=x^3+\left(2y\right)^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
3: \(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)\)
4: \(x^3-8y^3=x^3-\left(2y\right)^3=\left(x-2y\right)\left(x^2+2xy+4y^2\right)\)
Bài 5:
1: \(C=x^3+9x^2+27x+2027\)
\(=x^3+9x^2+27x+27+2000\)
\(=\left(x+3\right)^3+2000=\left(-23+3\right)^3+2000\)
=-8000+2000
=-6000
2: \(D=x^3+6x^2y+12xy^2+8y^3\)
\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=\left(x+2y\right)^3=\left(-2y+2y\right)^3=0\)
Bài 4:
1: \(\left(2x-3\right)^3-2x\left(2x+1\right)^2\)
\(=8x^3-36x^2+54x-27-2x\left(4x^2+4x+1\right)\)
\(=8x^3-36x^2+54x-27-8x^3-8x^2-2x=-44x^2+52x-27\)
2: \(\left(3x-1\right)^3-27x^2\cdot\left(x+1\right)\)
\(=27x^3-27x^2+9x-1-27x^3-27x^2\)
\(=-54x^2+9x-1\)
3: \(\left(2x+1\right)^3-8x\left(x-1\right)^2\)
\(=8x^3+12x^2+6x+1-8x\left(x^2-2x+1\right)\)
\(=8x^3+12x^2+6x+1-8x^3+16x^2-8x=28x^2-2x+1\)
Bài 3:
1: \(\left(2x+3y\right)^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3y+3\cdot2x\cdot\left(3y\right)^2+\left(3y\right)^3\)
\(=8x^3+36x^2y+54xy^2+27y^3\)
2: \(\left(3x+2y\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2y+3\cdot3x\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=27x^3+54x^2y+36xy^2+8y^3\)
3: \(\left(3x-2y\right)^3\)
\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot2y+3\cdot3x\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=27x^3-54x^2y+36xy^2-8y^3\)
Bài 2:
1: \(x\left(1-x\right)+\left(x-1\right)^2=x-x^2+x^2-2x+1=-x+1\)
2: \(\left(x-3\right)^2-x^2+10x-7\)
\(=x^2-6x+9-x^2+10x-7=4x+2\)
Bài 1:
1: \(\left(x+1\right)^2=x^2+2\cdot x\cdot1+1^2=x^2+2x+1\)
2: \(\left(4+x\right)^2=4^2+2\cdot4\cdot x+x^2=x^2+8x+16\)
3: \(\left(6-x\right)^2=6^2-2\cdot6\cdot x+x^2=36-12x+x^2\)
4: \(\left(x-5\right)^2=x^2-2\cdot x\cdot5+5^2=x^2-10x+25\)
