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 )

Từ \(4a^2+b^2=5ab\), ta có: \(4a^2-4ab-ab+b^2\)=0

Hay: (a-b) (4a-b)=0

Vì: 2a>b>0 nên 4a-b \(\ne\)0 .

Từ: (.) \(\Rightarrow\)

Từ: a-b=0 . Tức là: a=b

Thay a=b vào C ta được :

C= \(\frac{ab}{4a^2-b^2}=\frac{a^2}{4a^2-a^2}=\frac{1}{3}\)(do a\(\ne\)0)

a)\(2a^2-3ab+b^2\)

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

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

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

b)\(x^2-7x-30\)

=\(x^2-10x+3x-30\)

=\(x\left(x-10\right)+3\left(x-10\right)\)

=\(\left(x-10\right)\left(x+3\right)\)

c)\(6a^2-5ab-6b^2\)

=\(6a^2-9ab+4ab-6b^2\)

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

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

d)\(a^4+a^2+1\)

=\(a^4+2a^2-a^2+1\)

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

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

e)\(x^3+6x^2+11x+6\)

=\(x\left(x^2+6x+9+2\right)+6\) 

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

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

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

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

=5(a-b)²-10(a-b)= (a-b)(5a-5b-10)=5(a-b)(a-b-2)

a. \(2a^2+5ab-3b^2-7b-2\)

\(=\left(2a^2+6ab+2a\right)-\left(ab+3b^2+b\right)-\left(2a+6b+2\right)\)

\(=2a\left(a+3b+1\right)-b\left(a+3b+1\right)-2\left(a+3b+1\right)\)

\(=\left(2a-b-2\right)\left(a+3b+1\right)\)

b. \(2x^2-7xy+x+3y^2-3y\)

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

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

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

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

c. \(6x^2-xy-2y^2+3x-2y\)

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

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

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

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

4a²=4b²-4a+1

=(2a)²-2*2a*1+1²-4b²= (2a-1)²-(2b)²(2a-1-2b)(2a-1+2b)

a) = (xyz+xy) +(z+1) +(yz+zx)+(x+y)

 = xy(z+1) +(z+1)+z(x+y)+(x+y)

= (z+1)(xy+1)+(x+y)(Z+1)

=(z+1)(xy+1+x+y)

dễ mà bn

mk bk lm mà lm biếng gõ qá

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