(x + 2y)² - (x - y)²

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

= 3y(2x + y)

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

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

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

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

=>(x-\(\sqrt{5}\))²

=>(x-\(\sqrt{5}\)) (x-\(\sqrt{5}\))

Bài 1:

\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)

Bài 3:

\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)

Bài 1;

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

2) \(6x^2+12xy+6y^2=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)

3) \(2y^3+8y^3+8y=10y^3+8y=2y\left(5y^2+4\right)\)

4) \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

1) \(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

2) \(8x^2y-18y=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\)

3) \(24x^3-3=3\left(8x^3-1\right)=3\left(2x-1\right)\left(4x^2+2x+1\right)\)

Bài 3:

1) \(5x^2+10x+5-5y^2=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y\right]=5\left(x-y+1\right)\left(x+y+1\right)\)

2) \(3x^3-6x^2+3x-12xy^2=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=3x\left(x-2y-1\right)\left(x+2y-1\right)\)

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

4) \(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2-4x+4y\right)=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]=2x\left(x-y\right)\left(x+y-4\right)\)

81x⁴+4

=(9x²)²+2²

=(9x²)²+36x²+2²-36x²

=(9x²+2)²-(6x)²

=(9x²+2-6x)(9x²+2+6x)

\(\left(x^2+x+1\right)\left(x^2+x+5\right)-21=x^4+x^3+5x^2+x^3+x^2+5x+x^2+x+5-21=x^4+2x^3+7x^2+6x-16=\left(x-1\right)\left(x+2\right)\left(x^2+x+8\right)\)

\(=\left(x^2+x+1\right)\left(x^2+x+1+4\right)-21\)

\(=\left(x^2+x+1\right)^2+4\left(x^2+x+1\right)-21\)

\(=\left(x^2+x+1\right)^2-3\left(x^2+x+1\right)+7\left(x^2+x+1\right)-21\)

\(=\left(x^2+x+1\right)\left(x^2+x-2\right)+7\left(x^2+x-2\right)\)

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

\(=\left(x-1\right)\left(x-2\right)\left(x^2+x+8\right)\)

\(\left(x^2+x+1\right)\left(x^2+x+5\right)-21\)

\(=\left(x^2+x\right)^2+6\left(x^2+x\right)+5-21\)

\(=\left(x^2+x\right)^2+6\left(x^2+x\right)-16\)

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

\(=\left(x^2+x+8\right)\left(x+2\right)\left(x-1\right)\)

= x⁴ - 10x² + 25 + 144

= x⁴ - 10x² + 179

5 x 2 + 10xy – 4x – 8y = (5 x 2 + 10xy) – (4x + 8y)

= 5x(x + 2y) – 4(x + 2y) = (5x – 4)(x + 2y)

Đáp án cần chọn là: C

5 x 2   +   10 x y   –   4 x   –   8 y =   5 x 2   +   10 x y –   4 x   +   8 y =   5 x x   +   2 y   –   4 x   +   2 y =   5 x - 4 x + 2 y

Đáp án cần chọn là: C

\(a,=3\left(x-5\right)-x\left(x-5\right)=\left(3-x\right)\left(x-5\right)\\ b,=7\left(x^2-2xy+y^2\right)=7\left(x-y\right)^2\\ c,=\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)=\left(x-y\right)^2\left(x+y\right)^2\\ d,=\left(y^2-6y+9\right)-25x^2=\left(y-3\right)^2-25x^2=\left(y-5x-3\right)\left(y+5x-3\right)\)