1. \(=3x\left(2x+5\right)\)

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

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

1, = 3x.(2x + 5)

2. = (3x)² - 1² = (3x - 1).(3x +1 )

3, =(x² + 6x + 9) - y² = (x + 3)² - y² =(x + y -3 ). (x - y +3)

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

1)

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

2)

\(8x^3-12x^2+6x-2\\ =2\left(4x^3-6x^2+3x-1\right)\\ =2\left(4x^3-4x^2-2x^2+2x+x-1\right)\\ =2\left(4x^2\left(x-1\right)-2x\left(x-1\right)+\left(x-1\right)\right)\\ =2\left(x-1\right)\left(4x^2-2x+1\right)\)

1) \(y^2-4y+4-x^2\)

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

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

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

2) \(8x^3-12x^2+6x-1\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)

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

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

1: Đa thức này ko phân tích được nha bạn

2: \(x^2+8x+7\)

\(=x^2+x+7x+7\)

\(=x\left(x+1\right)+7\left(x+1\right)\)

\(=\left(x+1\right)\left(x+7\right)\)

3: \(x^2-6x-16\)

\(=x^2-8x+2x-16\)

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

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

4: \(4x^2-8x+3\)

\(=4x^2-2x-6x+3\)

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

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

5: \(3x^2-11x+6\)

\(=3x^2-9x-2x+6\)

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

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

1) \(2xy^3-6x^2+10xy\)

\(=2x.y^3-2x.3x+2x.5y\)

\(=2x\left(y^3-3x+5y\right)\)

\(=2x[y\left(y^2-5\right)-3x]\)

2) \(a^6-a^5-2a^3+2a^2\)

\(=\left(a^6-a^5\right)-\left(2a^3-2a^2\right)\)

\(=\left(a^5.a-a^5.1\right)-\left(2a^2.a-2a^2.1\right)\)

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

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

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

3: \(\left(a+b\right)^3-\left(a-b\right)^3\)

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

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

bài 1: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

\(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)

\(=\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)

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

Bài 2:

1: \(x^2y^2-8-1\)

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

\(=\left(xy-3\right)\left(xy+3\right)\)

2: \(x^3y-2x^2y+xy-xy^3\)

\(=xy\cdot x^2-xy\cdot2x+xy\cdot1-xy\cdot y^2\)

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

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

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

3: \(x^3-2x^2y+xy^2\)

\(=x\cdot x^2-x\cdot2xy+x\cdot y^2\)

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

4: \(x^2+2x-y^2+1\)

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

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

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

5: \(x^2+2x-4y^2+1\)

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

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

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

6: \(x^2-6x-y^2+9\)

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

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

13: =x(a^3-1)-b(a-1)

=x(a-1)(a^2+a+1)-b(a-1)

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

12: =(x-y)(x+y)-(x-y)

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

10: =3(x^2-4y^2)

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

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

8: =x^2+3x+4x+12=(x+3)(x+4)

9: =2x^2-6x-x+3=(x-3)(2x-1)

đặt y=x²+1

=>y²=(x²+1)²

y²=x⁴+2x²+1

đặt P(x)=x^4+6x^3+11x^2+6x+1

=x⁴+2x²+1+6x³+6x+9x²

=x⁴+2x+1+6x(x²+1)+9x²

thay y²=x⁴+2x²+1 và y=x²+1 ta được 

Q(y)=y²+6xy+9x²

=(y+3x)²

thay y=x²+1 ta được:

(x²+3x+1)²

vậy x^4+6x^3+11x^2+6x+1=(x²+3x+1)²

= (1 - x³ ) + ( 6x - 6x² ) 

= (1 - x ).(1 + x + x²) + 6x.(1 - x)

= (1 - x).(1+x+x² + 6x)

= (1 - x).(1 + 7x +x² )