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

b) \(7x^3y-3xyz-21x^2+9z=xy\left(7x^2-3z\right)-3\left(7x^2-3z\right)=\left(xy-3\right)\left(7x^2-3z\right)\)

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

a, 2x²y+2xy²-2x-2y = 2(x+y)(xy-1)

b, 7x³y-3xyz-21x²+9z = 7x²(xy-3) - 3z(xy-3) = (7x²-3z)(xy-3)

c, 4x + 4y - x²(x+y)= (x-2)(x+2)(x+y)

a) \(x^3-4x^2+2x+1\)

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

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

b) \(2x^3-7x^2+4x-3\)

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

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

\(6a^2-5ab-6b^2\)

\(=6a^2+4ab-9ab-6b^2\)

\(=2a.\left(3a+2b\right)-3b.\left(3a+2b\right)=\left(3a+2b\right).\left(2a-3b\right)\)

ý b: phân tích ra nhân tử rất xấu nhé bạn kiểm tra lại đề ạ

\(\left(5x-3y+4z\right)\left(5x-3y-4z\right)=\)

\(=\left(5x-3y\right)^2-16z^2=25x^2-30xy+9y^2-16z^2=\)

\(=25x^2-30xy+9y^2-16\left(x^2-y^2\right)=\)

\(=9x^2-30xy+25y^2=\left(3x-5y\right)^2\)

+) \(\left(2x-1\right)^2-\left(2x+3\right)\left(2x-1\right)=0\)

\(\left(2x-1\right)\left(2x-1-2x-3\right)=0\)

\(-4\left(2x-1\right)=0\)

\(x=\dfrac{1}{2}\)

+) \(\left(x+5\right)\left(x-2\right)-\left(x-3\right)\left(x+3\right)\)

\(=x^2-2x+5x-10-\left(x^2-9\right)\)

\(=3x-1\)

a, <=> (2x-1)(2x-1-2x-3)=0

<=> (2x-1).-4=0

<=> -8x + 4= 0

<=> -8x=-4 <=> x= 1/2