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

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

\(a,=7xy\left(x^2-2xy+y^2\right)=7xy\left(x-y\right)^2\\ b,=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\\ c,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\)

b: \(x^2-6x+xy-6y\)

\(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

c: \(2x^2+2xy-x-y\)

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

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

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

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

a, 4x² - 8x + 4 = (2x)² - 2.2x.2 + 2 = (2x - 2)²

b, x² - y² + 3x + 3y = (x² - y²) + (3x + 3y) = (x- y). (x + y) + 3.(x + y) = (x+y).(x- y + 3)

\(A=3x^2+6xy+3y^2-3z^2\)

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

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

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

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

`@` `\text {Ans}`

`\downarrow`

`a,`

`3x + 6xy + 3y - 3z`

`= 3(x + 2y + y - z)`

`b,`

`x+ xy - xz - xyz`

`= x(1 + y)*(1-z)`

a: 3x^2+6xy+3y^2-3z^2

=3(x^2+2xy+y^2-z^2)

=3[(x+y)^2-z^2]

=3(x+y+z)(x+y-z)

b: x+xy-xz-xyz

=x(y+1)-xz(y+1)

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

\(a,x\left(a-b\right)+2a-2b=x\left(a-b\right)+2\left(a-b\right)=\left(a-b\right)\left(x+2\right)\\ b,Sửa:ax+ay+5x+5y=a\left(x+y\right)+5\left(x+y\right)=\left(a+5\right)\left(x+y\right)\)

\(a,=\left(x+2\right)\left(a-b\right)\\ b,Sửa:ax+ay+5x+5y\\ =a\left(x+y\right)+5\left(x+y\right)\\ =\left(a+5\right)\left(x+y\right)\)

a) \(x\left(a-b\right)+2a-2b\)

\(=x\left(a-b\right)+\left(2a-2b\right)\)

\(=x\left(a-b\right)+2\left(a-b\right)\)

\(=\left(a-b\right)\left(x+2\right)\)

a Đề sai: )

b

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

c

\(4x^2-y^2+4x+1\\ =\left(2x\right)^2+2.2x.1+1-y^2\\ =\left(2x+1\right)^2-y^2\\ =\left(2x+1-y\right)\left(2x+1+y\right)\)

d

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

e

\(5x^2-10xy+5y^2-5z^2\\ =5\left(x^2-2xy+y^2-z^2\right)\\ =5\left[\left(x-y\right)^2-z^2\right]\\ =5\left(x-y-z\right)\left(x-y+z\right)\)

c: =(2x+1)^2-y^2

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

d: =x^2(x^2+2x+1)

=x^2(x+1)^2

e: =5(x^2-2xy+y^2-z^2)

=5[(x-y)^2-z^2]

=5(x-y-z)(x-y+z)

Câu 1: A

Câu 21: A

\(16,A\\ 17,C\\ 18,A\\ 19,C\\ 20,A\\ 21,A\)

1a