1: Ta có: \(x^3+x^2+x+1\)
\(=x^2\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+1\right)\)
2: Ta có: \(x^2y+xy^2-x-y\)
\(=xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(xy-1\right)\)
3: Ta có: \(x^2-xy+5x-5y\)
\(=x\left(x-y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+5\right)\)
4: Ta có: \(2x^2-x-6xy+3y\)
\(=x\left(2x-1\right)-3y\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x-3y\right)\)
5: Ta có: \(x^2+7x+7y-y^2\)
\(=\left(x+y\right)\left(x-y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
6: Ta có: \(x^2-2x-9y^2+6y\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-1\right)\)
7: Ta có: \(x^2+2xy+y^2-25\)
\(=\left(x+y\right)^2-25\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
8: Ta có: \(x^2y^2-x^2+8x-16\)
\(=\left(xy\right)^2-\left(x-4\right)^2\)
\(=\left(xy-x+4\right)\left(xy+x-4\right)\)
9: Ta có: \(5x^2-5xy-7x+7y\)
\(=5x\left(x-y\right)-7\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-7\right)\)
10: Ta có: \(5x^2-5y^2-4\left(x+y\right)^2\)
\(=5\left(x+y\right)\left(x-y\right)-4\left(x+y\right)^2\)
\(=\left(x+y\right)\left(5x-5y-4x-4y\right)\)
\(=\left(x+y\right)\left(x-9y\right)\)
11: Ta có: \(a^2-ac+b^2+2ab-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
12: Ta có: \(a^2-9b^2-ac+3bc\)
\(=\left(a-3b\right)\left(a+3b\right)-c\left(a-3b\right)\)
\(=\left(a-3b\right)\left(a+3b-c\right)\)
13: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
14: Ta có: \(x^3-5x^2-5x+1\)
\(=\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+1\right)\)
15: Ta có: \(3x^3-x^2-21x+7\)
\(=x^2\left(3x-1\right)-7\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x^2-7\right)\)
16: Ta có: \(x^3-4x^2+8x-8\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-2x+4\right)\)
