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 = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )

= 4x( ac + bc + a + b )

= 4x[ c( a + b ) + ( a + b ) ]

= 4x( a + b )( c + 1 )

B = ax - bx + cx - 3a + 3b - 3c

= x( a - b + c ) - 3( a - b + c )

= ( a - b + c )( x - 3 )

C = 2ax - bx + 3cx - 2a + b - 3c

= x( 2a - b + 3c ) - ( 2a - b + 3c )

= ( 2a - b + 3c )( x - 1 )

D = ax - bx - 2cx - 2a + 2b + 4c

= x( a - b - 2c ) - 2( a - b - 2c )

= ( a - b - 2c )( x - 2 )

E = 3ax² + 3bx² + ax + bx + 5a + 5b

= 3x²( a + b ) + x( a + b ) + 5( a + b )

= ( a + b )( 3x² + x + 5 )

F = ax² - bx² - 2ax + 2bx - 3a + 3b

= x²( a - b ) - 2x( a - b ) - 3( a - b )

= ( a - b )( x² - 2x - 3 )

= ( a - b )( x² + x - 3x - 3 )

= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]

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

d) \(ax^2-5x^2-ax+5x+a-5=\left(ax^2-ax+a\right)+\left(-5x^2+5x-5\right)\)

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

e) \(ax-bx-2cx-2a+2b+4c=x\left(a-b-2c\right)-2\left(a-b-2c\right)\)

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

ax^2 - 5x^2-ax+5x+a-5

=x^2(a-5) -x(a-5)+(a-5)

=(a-5)(x^2-x+1)

ax-bx-2cx-2a+2b+4c

=x(a-b-c) -2(a-b-c)

=(x-2)(a-b-c)

Nhập ĐT nên k tiện gõ công thức, thông cảm

d, \(ax^2-5x^2-ax+5x+a-5\)

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

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

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

e, \(ax-bx-2cx-2a+2b+4c\)

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

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

f, \(\left(4x^2-7x-50\right)^2-16x^4-56x^3-49x^2\)

\(=\left(4x^2-7x-50\right)\left(4x^2-7x-50\right)-16x^4-56x^3-49x^2\)

\(=16x^4-28x^3-200x^2-28x^3+49x^2+350x-200x^2+350x+2500-16x^4-56x^3-49x^2\)

\(=-112x^3-400x^2+700x+2500\)

\(=-\left(112x^2+400x^2-700x-2500\right)\)

\(=-\left(112x^3-280x^2+680x^2-1700x+1000x-2500\right)\)

\(=-\left[112x^2\left(x-2,5\right)+680x\left(x-2,5\right)+1000\left(x-2,5\right)\right]\)

\(=-\left[\left(x-2,5\right)\left(112x^2+680x+1000\right)\right]\)

\(=-\left[\left(x-2,5\right)\left(112x^2+280x+400x+1000\right)\right]\)

\(=-\left\{\left(x-2,5\right)\left[112x\left(x+2,5\right)+400\left(x+2,5\right)\right]\right\}\)

\(=-\left[\left(x-2,5\right)\left(x+2,5\right)\left(112x+400\right)\right]\)

\(=-\left[16\left(x-2,5\right)\left(x+2,5\right)\left(7x+25\right)\right]\)

Chúc bạn học tốt!!!

x³+64=x³+4³=(x+4)(x²-4x+4²)=(x+4)(x²-4x+16)

\(10x-25-x^2=-\left(x^2-10x+25\right)\)

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

10x - 25 - x²

= x²- 10x - 25

= - ( x² +10x +25)

= -(x² + 2.x.5+5² )

= - (x+5 )²

\(=\left(4-a+b\right)\left(4+a-b\right)\)

\(81x^6-y^6=\left(9x^3\right)^2-\left(y^3\right)^2=\left(9x^3-y^3\right)\left(9x^3+y^3\right)\)

\(2ax-bx+3cx-2a+b-3c\\ =x\left(2a-b+3c\right)-\left(2a-b+3c\right)\\ =\left(x-1\right)\left(2a-b+3c\right)\)

\(ax-bx-2cx-2a+2b+4c\\ =x\left(a-b-2c\right)-2\left(a-b-2c\right)\\ =\left(x-2\right)\left(a-b-2c\right)\)

\(3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\)

\(ax^2-bx^2-2ax+2bx-3a+3b\\ =x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a+b\right)\\ =\left(x^2-2x-3\right)\left(a+b\right)\\ =\left(x+1\right)\left(x-3\right)\left(a+b\right)\)

\(\Leftrightarrow x^2-10x+25=0\\ \Leftrightarrow\left(x-5\right)^2=0\\ \Leftrightarrow x=5\)

\(x^2-10x+25=0\)

\(x^2-10x+5^2=0\)

\(\left(x-5\right)^2=0\)