a) x² + x - 12 = x² - 3x + 4x - 12 = x(x - 3) + 4(x - 3) = (x - 3)(x + 4)

b) x² - x - 12 = x² + 3x - 4x - 12 = x(x + 3) - 4(x + 3) = (x + 3)(x - 4)

c) x² - 9x + 20 = x² - 4x - 5x + 20 = x(x - 4) - 5(x - 4) = (x - 4)(x - 5)

d) x² + 9x + 20 = x² + 4x + 5x + 20 = x(x + 4) + 5(x + 4) = (x + 4)(x + 5)

a,x^2+x-12=x^2-3x+4x-12

                 =x(x-3)+4(x-3)

                 =(x-3)*(x+4)

b) x² - x - 12 = x² + 3x - 4x - 12 = x(x + 3) - 4(x + 3) = (x + 3)(x - 4)

a) x² + x - 20 = x² - 4x + 5x - 20 = x(x - 4) + 5(x - 4) = (x - 4)(x + 5)

b) x² - x - 20 = x² + 4x - 5x - 20 = x(x + 4) - 5(x + 4) = (x + 4)(x - 5)

c) 2x² - 3x - 2 = 2x² - 4x + x - 2 = 2x(x - 2) + (x - 2) = (x - 2)(2x + 1)

d) 3x² + x - 2 = 3x² + 3x - 2x - 2 = 3x(x + 1) - 2(x + 1) = (x + 1)(3x - 2)

c ) \(x^2-7x+12\)

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

\(=x\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x-4\right)\left(x-3\right)\)

d ) \(x^2+7x+12\)

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

\(=x\left(x+3\right)+4\left(x+3\right)\)

\(=\left(x+4\right)\left(x+3\right)\)

\(1,\)

\(x^2+x-12\)

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

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

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

\(2,\)
\(x^2-9x+20\)

\(=x^2-4x-5x+20\)

\(=x\left(x-4\right)-5\left(x-4\right)\)

\(=\left(x-5\right)\left(x-4\right)\)

\(3,\)

\(x^2+x-20\)

\(=x^2-4x+5x-20\)

\(=x\left(x-4\right)+5\left(x-4\right)\)

\(=\left(x+5\right)\left(x-4\right)\)

Bài 2:

1)  \(x^2-4x+4=\left(x-2\right)^2\)

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

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

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

5) \(\dfrac{1}{25}x^2-64y^2=\left(\dfrac{1}{5}x-8y\right)\left(\dfrac{1}{5}x+8y\right)\)

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

Bài 2:

7) \(x^3+\dfrac{1}{27}=\left(x+\dfrac{1}{3}\right)\left(x^2+\dfrac{1}{3}x+\dfrac{1}{9}\right)\)

8) \(x^3+64=\left(x+4\right)\left(x^2+4x+16\right)\)

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

10) \(\left(a+b\right)^2-\left(a-b\right)^2=\left(a+b+a-b\right)\left(a+b-a+b\right)=2a\cdot2b=4ab\)

11) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

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

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

12) \(\left(6x-1\right)^2-\left(3x+2\right)^2=\left(6x-1+3x+2\right)\left(6x-1-3x-2\right)=\left(9x+1\right)\left(3x-3\right)\)

1:

1: ,4x^2-6x=2x(2x-3)

2: 9x^3y^2+3x^2y^2=3x^2y^2(3x+1)

3: x^3+2x^2+3x=x(x^2+2x+3)

4: 2x^2-4x=2x(x-2)

5: 3x-6y=3(x-2y)

6: x^2-3x=x(x-3)

7: 6x^2y+4xy^2+2xy

=2xy(3x+2y+1)

8: 5x^2(x-2y)-15x(x-2y)

=(x-2y)(5x^2-15x)

=5x(x-3)(x-2y)

9: =3(x-y)+5y(x-y)

=(x-y)(5y+3)

10: =(x-1)(3x+5)

11: =2(2x-1)-3(2x-1)

=-(2x-1)

a ) \(x^2-5x+6\)

\(=\left(x^2-2x\right)-\left(3x-6\right)\)

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

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

b )\(x^2+5x+6\)

\(=\left(x^2+2x\right)+\left(3x+6\right)\)

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

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

a.x^2 - 5x + 6

=x²-2x-3x+6

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

=(x-3)(x-2)

b.x^2 + 5x + 6

=x²+3x+2x+6

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

=(x+2)(x+3)

a: =4x^2+8x-3x-6

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

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

b: =3(3x^2-2x-1)

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

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

c: =2x^2-4x+x-2

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

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

d: =3x^2+3x-2x-2

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

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

e: =3x^2+9x+x+3

=3x(x+3)+(x+3)

=(x+3)(3x+1)

a) \(4x^2+5x-6\)

\(=4x^2+8x-3x-6\)

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

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

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

b) \(9x^2-6x-3\)

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

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

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

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

c) \(2x^2-3x-2\)

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

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

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

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

d) \(3x^2+x-2\)

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

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

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

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

e) \(3x^2+10x+3\)

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

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

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

x²-2.x.1/2 +(1/2)²-9/4

=(x-1/2)²-9/4

=(x-1/2)²-(3/2)²

=(x-1/2-3/2).(x-1/2+3/2)

=(x-2)(x+1)

\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)

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

\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)

\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)

\(=\left(13x-4y\right)\left(-7x-14y\right)\)

\(=-7\left(x+2y\right)\left(13x-4y\right)\)

9(x - 3y)² - 25(2x + y)²

= 3².(x - 3y)² - 5².(2x + y)²

= (3x - 9y)² - (10x + 5y)²

= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)

= (-7x - 14y)(13x - 4y)

= -7(x + 2y)(13x - 4y)