Bài 1:
1: \(\left(5x+1\right)^2=\left(5x\right)^2+2\cdot5x\cdot1+1^2=25x^2+10x+1\)
2: \(\left(2x+3\right)^2=\left(2x\right)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9\)
3: \(\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\)
4: \(\left(3x-2\right)^2=\left(3x\right)^2-2\cdot3x\cdot2+2^2=9x^2-12x+4\)
1: \(\left(2x+1\right)^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3\)
\(=8x^3+12x^2+6x+1\)
2: \(\left(3x+2\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2+3\cdot3x\cdot2^2+2^3\)
\(=27x^3+54x^2+36x+8\)
3: \(\left(2x-3\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2-3^3\)
\(=8x^3-36x^2+54x-27\)
4: \(\left(3x-1\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2-1^3=27x^3-27x^2+9x-1\)
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: \(x^3-8y^3=x^3-\left(2y\right)^3=\left(x-2y\right)\left(x^2+2xy+4y^2\right)\)
5: \(8x^3+1=\left(2x\right)^3+1^3=\left(2x+1\right)\cdot\left(4x^2-2x+1\right)\)
6: \(27y^3+1=\left(3y\right)^3+1^3=\left(3y+1\right)\left(9y^2-3y+1\right)\)
7: \(1-8x^3=1-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)
8: \(27x^3-1=\left(3x\right)^3-1^3=\left(3x-1\right)\left(9x^2+3x+1\right)\)
1: \(\left(3x\right)^2-y^2=\left(3x-y\right)\left(3x+y\right)\)
2: \(x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)
3: \(\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
Bài 2:
1: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)
\(=x^2+4x+4-\left(x^2+x-3x-3\right)\)
\(=x^2+4x+4-\left(x^2-2x-3\right)\)
\(=x^2+4x+4-x^2+2x+3=6x+7\)
2: \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)
\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\)
\(=x^2+2x-8-x^2+6x-9=8x-17\)
1: \(\left(x+2y\right)^3-\left(x-2y\right)^3\)
\(=x^3+6x^2y+12xy^2+8y^3-\left(x^3-6x^2y+12xy^2-8y^3\right)\)
\(=x^3+6x^2y+12xy^2+8y^3-x^3+6x^2y-12xy^2+8y^3\)
\(=12x^2y+16y^3\)
2: \(\left(y-x\right)^3-\left(2x-y\right)^3\)
\(=-\left(x-y\right)^3-\left(2x-y\right)^3\)
\(=-\left(x^3-3x^2y+3xy^2-y^3\right)-\left(8x^3-12x^2y+6xy^2-y^3\right)\)
\(=-x^3+3x^2y-3xy^2+y^3-8x^3+12x^2y-6xy^2+y^3\)
\(=-9x^3+15x^2y-9xy^2+2y^3\)
3: \(\left(2x+y\right)^3-2\left(y-x\right)^3\)
\(=8x^3+12x^2y+6xy^2+y^3+2\left(x-y\right)^3\)
\(=8x^3+12x^2y+6xy^2+y^3+2\left(x^3-3x^2y+3xy^2-y^3\right)\)
\(=8x^3+12x^2y+6xy^2+y^3+2x^3-6x^2y+6xy^2-2y^3\)
\(=10x^3+6x^2y+12xy^2-y^3\)
1: \(\left(x+5\right)\left(x^2-5x+25\right)-x\left(x-4\right)^2+16x\)
\(=x^3+5^3-x\left(x^2-8x+16\right)+16x\)
\(=x^3+125-x^3+8x^2-16x+16x=8x^2+125\)
2: \(\left(x+2\right)\left(x^2-2x+4\right)+\left(1-x\right)\left(1+x+x^2\right)\)
\(=x^3+2^3+1-x^3\)
=8+1
=9
em cần giải gấp bài 3 chi tiết mọi người giúp em với ạ. Làm bài dưới dạng phân số ạ em cần gấp
