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\(5x^2-4\left(x^2-2x+1\right)-5=\left(5x^2-5\right)-4\left(x-1\right)^2=5\left(x^2-1\right)-4\left(x-1\right)^2=5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=\left(x-1\right)\left[5\left(x+1\right)-4\left(x-1\right)\right]=\left(x-1\right)\left(5x+5-4x+4\right)=\left(x-1\right)\left(x+9\right)\)
\(=\left(x^2+4x-3\right)^2-5\left(x^2+4x-3\right)+6x^2\)
\(=x^4+16x^2+9+8x^3-24x-6x^2-5x^2-20x+15+6x^2\)
\(=x^4+8x^3+11x^2-44x+24\)
\(=\left(x^4-x^3\right)+\left(9x^3-9x^2\right)+\left(20x^2-20x\right)-\left(24x-24\right)\)
\(=x^3\left(x-1\right)+9x^2\left(x-1\right)+20x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+9x^2+20x-24\right)\)
\(3x^2-5x-8\)
\(=3x^2+3x-8x-8\)
\(=\left(3x^2+3x\right)-\left(8x+8\right)\)
\(=3x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(3x-8\right)\left(x+1\right)\)
3x2 - 5x - 8 = 3x2 + 3x - 8x - 8 = ( 3x2 + 3x ) - ( 8x + 8 )
= 3x( x + 1 ) - 8( x + 1 ) = ( 3x - 8 )( x + 1 )
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)\(25-\left(x^2-4xy+4y^2\right)=5^2-\left(x-2y\right)^2=\left(x-2y+5\right)\left(5-x+2y\right)\)
\(5x^2-x+y-5y^2\)
\(=\left(5x^2-5y^2\right)-\left(x-y\right)\)
\(=5\left(x^2-y^2\right)-\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left[5\left(x+y\right)-1\right]\)
\(=\left(x-y\right)\left(5x+5y-1\right)\)
a) x2+x-2
= x2-x+2x-2
= x(x-1)+2(x-1)
= (x+2)(x-1)
b) 2x2+5x+3
= 2x2+2x+3x+3
= 2x(x+1)+3(x+1)
= (2x+3)(x+1)
c) 3x2+5x-2
= 3x2+6x-1x-2
= 3x(x+2)-1(x+2)
= (3x-1)(x+2)