\(5x^2-4\left(x^2-2x+1\right)-5=\left(5x^2-5\right)-4\left(x-1\right)^2=5\left(x^2-1\right)-4\left(x-1\right)^2=5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=\left(x-1\right)\left[5\left(x+1\right)-4\left(x-1\right)\right]=\left(x-1\right)\left(5x+5-4x+4\right)=\left(x-1\right)\left(x+9\right)\)

\(= \)\(5x^2-4x^2+8x-4-5\)

\(=\)\(x^2+8x-9\)

\(=x^2+9x-x-9\)

\(=(x-1)(x+9)\)

\(5x^2-4\left(x^2-2x+1\right)-5\)

\(=5x^2-4x^2+8x-4-5\)

\(=x^2+8x-9\)

\(=\left(x+9\right)\left(x-1\right)\)

\(=\left(x^2+4x-3\right)^2-5\left(x^2+4x-3\right)+6x^2\)

\(=x^4+16x^2+9+8x^3-24x-6x^2-5x^2-20x+15+6x^2\)

\(=x^4+8x^3+11x^2-44x+24\)

\(=\left(x^4-x^3\right)+\left(9x^3-9x^2\right)+\left(20x^2-20x\right)-\left(24x-24\right)\)

\(=x^3\left(x-1\right)+9x^2\left(x-1\right)+20x\left(x-1\right)-24\left(x-1\right)\)

\(=\left(x-1\right)\left(x^3+9x^2+20x-24\right)\)

\(3x^2-5x-8\)

\(=3x^2+3x-8x-8\)

\(=\left(3x^2+3x\right)-\left(8x+8\right)\)

\(=3x\left(x+1\right)-8\left(x+1\right)\)

\(=\left(3x-8\right)\left(x+1\right)\)

3x² - 5x - 8 = 3x² + 3x - 8x - 8 = ( 3x² + 3x ) - ( 8x + 8 )

= 3x( x + 1 ) - 8( x + 1 ) = ( 3x - 8 )( x + 1 )

3x²-5x-8

=3x²+3x-8x-8

=3x(x+1)-8(x+1)

=(x+1)((3x-8)

=5(x²-9)

=5(x²-3²)

=5(x-3)(x+3)

Phân tích đa thức thành nhân tử:

a) \(xy+y^2-x-y=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)

b) \(25-x^2+4xy-4y^2=25-\left(x^2-4xy+4y^2\right)=25-\left(x-2y\right)^2\)

\(=\left(5-x+2y\right)\left(5+x-2y\right)\)

Rút gọn biểu thức;

\(A=\left(6x+1\right)^2+\left(3x-1\right)^2-2\left(3x-1\right)\left(6x+1\right)\)

\(=\left[\left(6x+1\right)-\left(3x-1\right)\right]^2=\left(6x+1-3x+1\right)=\left(3x+2\right)^2\)

Tìm a để đa thức.. Bạn chia cột dọ thì da

\(xy+y^2-x-y=\left(xy+y^2\right)-\left(x+y\right)=y\left(x+y\right)-\left(x+y\right)=\left(y-1\right)\left(x+y\right)\)b)\(25-\left(x^2-4xy+4y^2\right)=5^2-\left(x-2y\right)^2=\left(x-2y+5\right)\left(5-x+2y\right)\)

x^2-5x-14= x^2 - 7x +2x -14=  x(x-7) +2(x-7)=(x-7)(x+2)

x²-5x-14=x²-7x+2x-14=x(x-7)+2(x-7)=(x+2)(x+7)

\(x^2-5x-14\)

\(=x^2+2x-7x-14\)

\(=x\left(x+2\right)-\left(7x+14\right)\)

\(=x\left(x+2\right)-7\left(x+2\right)\)

\(=\left(x-7\right)\left(x+2\right)\)

\(5x^2-x+y-5y^2\)

\(=\left(5x^2-5y^2\right)-\left(x-y\right)\)

\(=5\left(x^2-y^2\right)-\left(x-y\right)\)

\(=5\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)

\(=\left(x-y\right)\left[5\left(x+y\right)-1\right]\)

\(=\left(x-y\right)\left(5x+5y-1\right)\)