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

b) \(9x^2+6x-4y^2+4y=\left(9x^2+6x+1\right)-\left(4y^2-4y+1\right)=\left(3x+1\right)^2-\left(2y-1\right)^2=\left(3x+1-2y+1\right)\left(3x+1+2y-1\right)=\left(3x-2y+2\right)\left(3x+2y\right)\)

a: \(5x^2-4\left(x^2-2x+1\right)-5\)

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

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

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

b: \(9x^2+6x-4y^2+4y\)

\(=\left(3x+2y\right)\left(3x-2y\right)+2\left(3x+2y\right)\)

\(=\left(3x+2y\right)\left(3x-2y+2\right)\)

\(A=-x-z\left(x-y\right)+y=-x-xz+zy+y=-x\left(1+z\right)+y\left(1+z\right)=\left(1+z\right)\left(y-x\right)\)

A = -(x-y)-z(x-y)=(x-y)(-1-z)=(y-x)(z+1)

A = -x - z(x - y) + y

A = -x - zx + zy + y

A = -(-x - zx + zy + y)

A = x + zx - zy - y

A = x + zx - y - zy

A = x(1 + z) - y(1 + z)

A = (x - y)(1 + z)

\(\left(x+y\right)^2+3\left(x+y\right)-10=\left[\left(x+y\right)^2+2\left(x+y\right).\dfrac{3}{2}+\dfrac{9}{4}\right]-\dfrac{49}{4}\)

\(=\left(x+y+\dfrac{3}{2}\right)^2-\dfrac{49}{4}=\left(x+y+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x+y+\dfrac{3}{2}+\dfrac{7}{2}\right)=\left(x+y-2\right)\left(x+y+5\right)\)

\(\left(x+y\right)^2+3\left(x+y\right)-10\)

\(=\left(x+y\right)^2+5\left(x+y\right)-2\left(x+y\right)-10\)

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

\(=x\left[x^2\left(x-y\right)^2-36y^2\right]\\ =x\left[x\left(x-y\right)-6y\right]\left[x\left(x-y\right)+6y\right]\\ =x\left(x^2-xy-6y\right)\left(x^2-xy+6y\right)\)

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

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

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

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

\(\left(x+y+z\right)^2+\left(x+y-z\right)^2-4z^2=\left(x+y+z\right)^2+\left(x+y-z-2z\right)\left(x+y-z+2z\right)=\left(x+y+z\right)^2+\left(x+y-3z\right)\left(x+y+z\right)=\left(x+y+z\right)\left(x+y+z+x+y-3z\right)=\left(x+y+z\right)\left(2x+2y-2z\right)=2\left(x+y+z\right)\left(x+y-z\right)\)

Ta có:

 (x + y + z)² + (x + y – z)² – 4z²

^{\(=\left(x+y-z\right)^2+\left(x+y-z\right)\left(x+y+3z\right)\)}

​\(=\left(x+y-z\right)\left(x+y+3z+x+y-z\right)\)​

\(\left(x+y+z\right)^2+\left(x+y-z\right)^2-4z^2\)

\(=x^2+y^2+z^2+2xy+2yz+2xz+x^2+y^2+z^2+2xy-2xz-2yz-4z^2\)

\(=2x^2+2y^2-2z^2+4xy\)

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

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

\(\left(x+y\right)\left(x+2y\right)\left(x+3y\right)\left(x+4y\right)+y^4\)

\(=\left(x^2+5xy+4y^2\right)\left(x^2+5xy+6y^2\right)+y^4\)

\(=\left(x^2+5xy\right)^2+10y^2\left(x^2+5xy\right)+24y^4+y^4\)

\(=\left(x^2+5xy+5y^2\right)^2\)

Ta có: ( xy+1)^2 - (x+y)^2

= x^2.y^2 + 2xy + 1^2 - x^2 -2xy - y^2

= x^2. y^2 - x^2 - y^2 +1

= x^2( y^2 - 1) - (y^2 -1)

= (x^2 - 1)(y^2-1) 

\(2x^2+x-6\)

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

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

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

Tham Khảo

2x² + x - 6

= 2x² + 4x - 3x - 6

= 2x(x + 2) - 3(x - 2)

= (2x - 3)(x + 2)