a: \(x^2-y^2+3x+3y\)

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

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

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

b: Sửa đề: \(x^2-4y^2+4x+4\)

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

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

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

\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)

1: \(6x^2y-9xy^2+3xy\)

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

2: \(\left(4-x\right)^2-16\)

\(=\left(4-x-4\right)\left(4-x+4\right)\)

\(=-x\cdot\left(8-x\right)\)

3: \(x^3+9x^2-4x-36\)

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

\(=\left(x+9\right)\left(x-2\right)\left(x+2\right)\)

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

2) \(\left(4-x\right)^2-16=\left(4-x\right)^2-4^2=\left(4-x-4\right)\left(4-x+4\right)=-x\left(8-x\right)\)

3) \(x^3+9x^2-4x-36\\ =\left(x^3-2x^2\right)+\left(11x^2-22x\right)+\left(18x-36\right)\\ =x^2\left(x-2\right)+11x\left(x-2\right)+18\left(x-2\right)\\ =\left(x^2+11x+18\right)\left(x-2\right)\\ =\left[\left(x^2+2x\right)+\left(9x+18\right)\right]\left(x-2\right)\\ =\left[x\left(x+2\right)+9\left(x+2\right)\right]\left(x-2\right)\\ =\left(x+2\right)\left(x+9\right)\left(x-2\right)\)

Câu b đề sai nha bạn.

a) \(x^3+9x^2+27x+27=\left(x+3\right)^3\)

b) \(3\sqrt{3x^3}+18x^2+12\sqrt{3x}+8=\left(\sqrt{3x}+2\right)^3\)

c) \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}-x\right)\left(\dfrac{1}{2}+x\right)\)

=(x-5)(x-4)

\(=x^2-4x-5x+20=\left(x-4\right)\left(x-5\right)\)

\(x^2-9x+20=\left(x^2-4x\right)-\left(5x-20\right)=x\left(x-4\right)-5\left(x-4\right)=\left(x-4\right)\left(x-5\right)\)

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

\(=x\cdot x-x\cdot9\)

=x(x-9)

(x-1)*x^2*(x^3+x^2-9)

x⁴(x² - 1) - 9x²(x - 1)

=x⁴(x - 1)(x + 1) - 9x²(x -1)

=(x - 1)(x⁵ + x⁴ - 9x²)

= x⁴(x²-1)-9x²(x-1)

=x⁴(x-1)(x+1)-9x²(x-1)

=(x⁴(x+1)-9x²)(x-1)

=(x⁵+x⁴-9x²)(x-1)

1: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

2: \(x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\)

3: \(9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\)

4: \(x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

\(1,x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\\ 2,x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\\ 3,9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\\ 4,x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

 1,x−9=(√x−3)(√x+3)

2,x−16=(√x−4)(√x+4)

3,9x−1=(3√x−1)(3√x+1)

4,x√x+1=(√x+1)(x−√x+1