Bài 1:
\(1.\left(x+1\right)^2=x^2+2\cdot x\cdot1+1^2=x^2+2x+1\\ 2.\left(4+x\right)^2=4^2+2\cdot4\cdot x+x^2=16+8x+x^2\\ 3.\left(6-x\right)^2=6^2-2\cdot6\cdot x+x^2=36-12x+x^2\\ 4.\left(x-5\right)^2=x^2-2\cdot x\cdot5+5^2=x^2-10x+25\\ 5.\left(5x+1\right)^2=\left(5x\right)^2+2\cdot5x\cdot1+1^2=25x^2+10x+1\\ 6.\left(2x+3\right)^2=\left(2x\right)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9\\ 7.\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\\ 8.\left(3x-2\right)^2=\left(3x\right)^2-2\cdot3x\cdot2+2^2=9x^2-12x+4\\ 9.\left(x+2y\right)^2=x^2+2\cdot x\cdot2y+\left(2y\right)^2=x^2+4xy+4y^2\\ 10.\cdot\left(x+5y\right)^2=x^2+2\cdot x\cdot5y+\left(5y\right)^2=x^2+10xy+25y^2\\ 11.\left(x-2y\right)^2=x^2-2\cdot x\cdot2y+\left(2y\right)^2=x^2-4xy+4y^2\\ 12.\left(2x-y\right)^2=\left(2x\right)^2-2\cdot2x\cdot y+y^2=4x^2-4xy+y^2\)
Bài 4:
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
3: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)
\(=x^2+4x+4-\left(x^2-2x-3\right)\)
\(=x^2+4x+4-x^2+2x+3\)
=6x+7
4: \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)
\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\)
\(=x^2+2x-8-x^2+6x-9\)
=8x-17
Bài 2:
1: \(x^2-4=x^2-2^2=\left(x-2\right)\left(x+2\right)\)
2: \(1-4x^2=1-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
3: \(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)
4: \(9-25x^2=3^2-\left(5x\right)^2=\left(3-5x\right)\left(3+5x\right)\)
5: \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)
6: \(9x^2-36=9\left(x^2-4\right)=9\left(x-2\right)\left(x+2\right)\)