a) a³ - a²c + a²b - abc

= a( a² - ac + ab - bc )

= a[ a( a - c ) + b( a - c ) ]

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

b) ( x² + 1 )² - 4x²

= ( x² + 1 )² - ( 2x )²

= ( x² - 2x + 1 )( x² + 2x + 1 )

= ( x - 1 )²( x + 1 )²

c) x² - 10x - 9y² + 25

= ( x² - 10x + 25 ) - 9y²

= ( x - 5 )² - ( 3y )²

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

d) 4x² - 36x + 56

= 4( x² - 9x + 14 )

= 4( x² - 7x - 2x + 14 )

= 4[ x( x - 7 ) - 2( x - 7 ) ]

= 4( x - 7 )( x - 2 )

a,\(a^3-a^2c+a^2b-abc\)

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

\(=a\left[a\left(a-c\right)+b\left(a-c\right)\right]\)

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

b,\(\left(x^2+1\right)^2-4x^2\)

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

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

c,\(x^2-10x-9y^2+25\)

\(=\left(x^2-10x+25\right)-9y^2\)

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

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

d,\(4x^2-36x+56\)

\(=4\left(x^2-9x+14\right)\)

\(=4\left(x^2-7x-2x+14\right)\)

\(=4\left(x-7\right)\left(x-2\right)\)

Bài 1: (2 điểm) Phân tích các đa thức sau thành nhân tử

a) a³ – a²c + a²b – abc

= a(a² - ac + ab - bc)

= a[a(a - c) + b(a - c)]

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

b) (x² + 1)² – 4x²

= (x² + 1)² – (2x)²

= (x² + 1 - 2x)(x² + 1 + 2x)

= (x - 1)². (x + 1)²

c) x² – 10x – 9y² + 25

= (x² - 10x + 25) - 9y²

= (x - 5)² - (3y)²

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

d) 4x² – 36x + 56

= 4x² - 28x - 8x + 56

= (4x² - 28x) - (8x - 56)

= 4x(x - 7) - 8(x - 7)

= (x - 7)(4x - 8)

= 4(x - 7)(x - 2)

a) \(12xy-4x^2-9y^2=-\left(4x^2-12xy+9y^2\right)\)

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

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

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

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

douma dễ mà bạn

`#040911`

`a)`

`196 - a^2 + 2ab - b^2`

`= 196 - (a^2 - 2ab + b^2)`

`= 196 - (a - b)^2`

`= 14^2 - (a - b)^2`

`= (14 - a + b)(14 + a - b)`

`b)`

`a^2 + 6a - 4b^2 + 9`

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

`= [ (a)^2 + 2*a*3 + 3^2] - (2b)^2`

`= (a + 3)^2 - (2b)^2`

`= (a + 3 - 2b)(a + 3 + 2b)`

`c)`

`4x - 4 + 9y^2 - x^2`

`=  9y^2 - (x^2 - 4x + 4)`

`= (3y)^2 - [ (x)^2 - 2*x*2 + 2^2]`

`= (3y)^2 - (x - 2)^2`

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

`d)`

`5x^2 - 10x + 5 - 45t^2`

`= 5*(x^2 - 2x + 1 - 9t^2)`

`= 5*[ (x^2 - 2x + 1) - 9t^2]`

`= 5*{ [(x)^2 - 2*x*1 + 1^2] - (3t)^2}`

`= 5*[ (x - 1)^2 - (3t)^2]`

`= 5*(x - 1 - 3t)(x - 1 + 3t)`

`e)`

`x^2 - 36y^2t^2 - 10x +25`

`= (x^2 - 10x + 25) - 36y^2t^2`

`= [ (x)^2 - 2*x*5 + 5^2] - (6yt)^2`

`= (x - 5)^2 - (6yt)^2`

`= (x - 5 - 6yt)(x - 5 + 6yt)`

a: =196-(a^2-2ab+b^2)

=196-(a-b)^2

=(14-a+b)(14+a-b)

b: \(=\left(a^2+6a+9\right)-4b^2\)

\(=\left(a+3\right)^2-4b^2\)

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

c: \(=9y^2-\left(x^2-4x+4\right)\)

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

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

d: \(=5\left(x^2-2x+1-9t^2\right)\)

\(=5\left[\left(x-1\right)^2-\left(3t\right)^2\right]\)

\(=5\left(x-1-3t\right)\cdot\left(x-1+3t\right)\)

e: \(=x^2-10x+25-36y^2t^2\)

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

\(=\left(x-5-6yt\right)\left(x-5+6yt\right)\)

Giúp mình với ạ,cảm ơn mọi người

b: Ta có: \(B=x^2+4x+9y^2-6y-1\)

\(=x^2+4x+4+9y^2-6y+1-6\)

\(=\left(x+2\right)^2+\left(3y-1\right)^2-6\ge-6\forall x,y\)

Dấu '=' xảy ra khi x=-2 và \(y=\dfrac{1}{3}\)

mình chỉ phân tích thôi

a) 6x(4-x)+x-4

=6x(4-x)-(4-x)

=(6x-1)(4-x)

c) 25x^2-10x+1-16z^2

=(5x-1)^2-16z^2

=(5x-1-4z)(5x-1+4z)

ban xem lại đề bài câu b đi chắc là sai đó

còn các câu trên bạn tự làm nhé

Thực hiện phép tính:

a) (2x-3y)(4x²+6xy+9y²)

=8x³-27y³

b) (6x³+3x²+4x+2):(3x²+2)

=(3x²+2)(2x+1):(3x²+2)

=2x+1

c) (x+2)²+(3-x)-2(x+3)(x-3)

=x²+4x+4+3-x-2x²+18

=-x²+4x+25

Bài 2: 

a: 6x(4-x)+(x-4)

=6x(4-x)-(4-x)

=(4-x)(6x-1)

b: \(=x^2-1+y\left(x^2-1\right)\)

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

c: \(=\left(5x-1\right)^2-\left(4z\right)^2\)

=(5x-1-4z)(5x-1+4z)