a: =4(x-2)(x+1)+4(x-2)^2+(x+1)^2

=(2x-4)^2+2*(2x-4)(x+1)+(x+1)^2

=(2x-4+x+1)^2=(3x-3)^2=9(x-1)^2

b: =x^7(x^2-1)-x^5(x+1)+x^3(x+1)+(x^2-1)

=(x+1)[x^7(x-1)-x^5+x^3+x-1]

=(x+1)[x^7(x-1)-x^3(x-1)(x+1)+(x-1)]

=(x+1)(x-1)(x^7-x^4-x^3+1)

=(x+1)(x-1)(x^3-1)(x^4-1)

=(x+1)(x-1)^2*(x^2+x+1)(x^2+1)(x-1)(x+1)

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

\(A=\left(x^2+x\right)^2+2\left(x^2+x\right)+1=\left(x^2+x+1\right)^2\)

\(B=\left(x-a\right)^4-\left(x+a\right)^4=\left[\left(x-a\right)^2\right]^2-\left[\left(x+a\right)^2\right]^2\)

\(=\left[\left(x-a\right)^2-\left(x+a\right)^2\right]\left[\left(x-a\right)^2+\left(x+a\right)^2\right]\)

\(=\left(x-a-x-a\right)\left(x-a+x+a\right)\left(x^2-2xa+a^2+x^2+2ax+a^2\right)\)

\(=-2a.2x\left(2x^2+2a^2\right)=-8ax\left(x^2+a^2\right)\)

\(x^4+1\)

\(=x^4+2x^2+1-2x^2\)

\(=\left(x^2+1\right)^2-\left(x\sqrt{2}\right)^2\)

\(=\left(x^2-x\sqrt{2}+1\right)\left(x^2+x\sqrt{2}+1\right)\)

______

\(4x^4y^4+1\)

\(=4x^4y^4+4x^2y^2+1-4x^2y^2\)

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

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

______

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

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

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

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

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

______

\(x^2+3xy+2y^2\)

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

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

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

a: \(x^2+2x+1+4x+4\)

\(=\left(x^2+2x+1\right)+\left(4x+4\right)\)

\(=\left(x+1\right)^2+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x+1+4\right)\)

\(=\left(x+1\right)\left(x+5\right)\)

b: Sửa đề: \(2x^3+6x^2+x^2+3x\)

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

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

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

c: \(\dfrac{1}{2}x^2+\dfrac{1}{4}x+\dfrac{1}{4}x+1\)

\(=\dfrac{1}{4}x\left(\dfrac{1}{4}x+1\right)+\left(\dfrac{1}{4}x+1\right)\)

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

\(a,=\left(x-1\right)^4-2\left(x-1\right)^2+1\\ =\left[\left(x-1\right)^2-1\right]^2\\ =\left(x^2-2x-2\right)^2\\ b,=\left[\left(x+1\right)\left(x+5\right)\right]\left[\left(x+2\right)\left(x+4\right)\right]-4\\ =\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)+36\\ =\left(x^2+6x+4\right)\left(x^2+6x+9\right)\\ =\left(x+3\right)^2\left(x^2+6x+4\right)\)

\(16-x^2\)

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

\(---\)

\(16-3x+1^2\) (kt lại đề bài nhé)

\(x^4y^4+4x^2y^2+4\)

\(=\left[\left(xy\right)^2\right]^2+2\cdot\left(xy\right)^2\cdot2+2^2\)

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

\(---\)

\(y^2-4y+4-x^2\)

\(=y^2-2\cdot y\cdot2+2^2-x^2\)

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

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