19: \(x^3-4x^2+12x-27\)
\(=\left(x^3-27\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+9-4x\right)=\left(x-3\right)\left(x^2-x+9\right)\)
21: \(x^2-9y^2+4x-12y\)
=(x-3y)(x+3y)+4(x-3y)
=(x-3y)(x+3y+4)
22: \(a^2+2a+2b-b^2\)
\(=\left(a^2-b^2\right)+2\left(a+b\right)\)
=(a+b)(a-b)+2(a+b)
=(a+b)(a-b+2)
23: \(x^2+9y^2-9+6xy\)
\(=\left(x^2+6xy+9y^2\right)-9\)
\(=\left(x+3y\right)^2-3^2\)
=(x+3y-3)(x+3y+3)
24: \(x^3-3x^2-3x+1\)
\(=\left(x^3+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\cdot\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
25: \(4\left(x+y\right)^2-9\left(x-y\right)^2\)
\(=\left(2x+2y\right)^2-\left(3x-3y\right)^2\)
=(2x+2y-3x+3y)(2x+2y+3x-3y)
=(-x+5y)(5x-y)
26: \(25y^2-x^2-6x-9\)
\(=25y^2-\left(x^2+6x+9\right)\)
\(=\left(5y\right)^2-\left(x+3\right)^2\)
=(5y-x-3)(5y+x+3)
27: \(x^3+4x^2-8x-8\)
\(=\left(x^3-8\right)+4x^2-8x\)
\(=\left(x-2\right)\left(x^2+2x+4\right)+4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4+4x\right)=\left(x-2\right)\left(x^2+6x+4\right)\)
28: \(x^3+27-\left(2x+1\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-\left(2x+1\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-2x-1\right)=\left(x+3\right)\left(x^2-5x+8\right)\)
29: \(\left(x^2+y\right)^2-2x^2-2y+1\)
\(=\left(x^2+y\right)^2-2\left(x^2+y\right)+1\)
\(=\left(x^2+y-1\right)^2\)
giúp mình câu này với ạ
giúp mình câu này với ạ,ghi rõ luôn ạ