a) x⁴ + 2x³ + 2x² + 2x + 1

=[ (x²)² + 2.x².x + x² ] + (x² + 2.x.1 + 1²)

=(x² + x)² + (x + 1)²

=[x(x + 1)]² + (x + 1)²

=x²(x + 1)² + (x + 1)²

=(x² + 1)(x + 1)²

b) x² - 2x - 4y² - 4y

= [x² - (2y)²] - 2(x - 2y)

= (x - 2y)(x + 2y) - 2(x - 2y)

= (x + 2y - 2)(x - 2y)

Câu này số xấu không phân tích được nhân tử lun

\(x^3\left(2+x\right)^2-\left(x+2\right)^2+1-x^3\\ =\left(x+2\right)^2\left(x^3-1\right)-\left(x^3-1\right)\\ =\left[\left(x+2\right)^2-1\right]\left(x^3-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x^2+4x+3\right)=\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x^2+x+1\right)\)

\(x^3-4x^2+8x-8=x^2\left(x-2\right)-2x\left(x-2\right)+4\left(x-2\right)=\left(x-2\right)\left(x^2-2x+4\right)\)

\(x^3-4x^2+8x-8\)

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

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

\(x^2\left(x-3\right)-4x+12=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)

=x²(x-3)-4x+3.4

=x²(x-3)-4(x+3)

=x²(x-3)+4(x-3)

=(x-3)(x²+4)

=(x-3)(x²+2²)

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

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

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

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

bạn có thể viết rõ hơn ko

x^4+x^2y^2+y^4

=x^4+2x^2y^2+y^4-x^2y^2

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

=(x^2-xy+y^2)(x^2+xy+y^2)

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

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

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

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

(x-2)*(x-1)

(x-2)(x-1)

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

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

=x²-9

=x²-3² =(x-3)(x+3)