Rút gọn thôi chứ phân tích sao được ._.

( x - 3 )² - ( 4x + 5 )² - 9( x + 1 )² - 6( x - 3 )( x + 1 )

= x² - 6x + 9 - ( 16x² + 40x + 25 ) - 9( x² + 2x + 1 ) - 6( x² - 2x - 3 )

= x² - 6x + 9 - 16x² - 40x - 25 - 9x² - 18x - 9 - 6x² + 12x + 18

= -30x² - 52x - 7

Sửa đề lại 1 chút là phân tích được mà bn Quỳnh:))

Ta có: \(\left(x-3\right)^2-\left(4x+5\right)^2+9\left(x+1\right)^2-6\left(x-3\right)\left(x+1\right)\)

\(=\left[\left(x-3\right)^2-6\left(x-3\right)\left(x+1\right)+9\left(x+1\right)^2\right]-\left(4x+5\right)^2\)

\(=\left(x-3-9x-9\right)^2-\left(4x+5\right)^2\)

\(=\left(8x+12\right)^2-\left(4x+5\right)^2\)

\(=\left(4x+7\right)\left(12x+17\right)\)

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

a: \(a\left(x-y\right)-b\left(y-x\right)+c\left(x-y\right)\)

\(=a\left(x-y\right)+b\left(x-y\right)+c\left(x-y\right)\)

\(=\left(x-y\right)\left(a+b+c\right)\)

b: \(a^m-a^{m+2}\)

\(=a^m-a^m\cdot a^2\)

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

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

Ta có : (x³ + 3x + 1)(x³ + 3x + 2) - 6

= (x³ + 3x + 1,5 - 0,5)(x³ + 3x + 1,5 + 0,5) - 6

= (x³ + 3x + 1,5)² - 0,5² - 6

= (x³ + 3x + 1,5)² - 6,25

= (x³ + 3x + 1,5 - 2,5) (x³ + 3x + 1,5 + 2,5)

= (x³ + 3x - 1) (x³ + 3x + 3)

(x^2 - 2x)(x^2 - 2x - 1) - 6

đặt x^2 - 2x = a              

= a(a - 1) - 6

= a^2 - a - 6

= a^2 - 3a + 2a - 6

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

= (a + 2)(a - 3)

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

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

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

\(=ax^2+a-a^2x-x\)

\(=ax\left(x-a\right)-\left(x-a\right)\)

\(=\left(x-a\right)\left(ax-1\right)\)

       \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right).\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1-3xy\right]\)

\(=\left(x+y-1\right).\left[x^2+2xy+y^2+x+y+1-3xy\right]\)

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

Chúc bạn học tốt.

\(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(\Leftrightarrow\left(x+y-1\right)\left(\left(x+y\right)^2+\left(x+y\right).1+1^2\right)-3xy\left(x+y-1\right)\)

\(\Leftrightarrow\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)

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

(x - 5)² - 4(x - 3)² + 2(2x - 1)(x - 5) + (2x - 1)²

= [(x - 5)² + 2(2x - 1)(x - 5) + (2x - 1)²) - [2(x - 3)]²

= (x - 5 + 2x - 1)² - (2x - 6)²

= (3x - 6)² - (2x - 6)²

= (3x - 6 - 2x + 6)(3x - 6 + 2x - 6) = x(5x - 12)

( x - 5 )² - 4( x - 3 )² + 2( 2x - 1 )( x - 5 ) + ( 2x - 1 )²

= [ ( x - 5 )² + 2( 2x - 1 )( x - 5 ) + ( 2x - 1 )² ] - 2²( x - 3 )²

= ( x - 5 + 2x - 1 )² - ( 2x - 6 )²

= ( 3x - 6 )² - ( 2x - 6 )²

= ( 3x - 6 - 2x + 6 )( 3x - 6 + 2x - 6 )

= x( 5x - 12 )

\(\left(x-5\right)^2-4\left(x-3\right)^2+2\left(2x-1\right)\left(x-5\right)+\left(2x-1\right)^2\)

\(=\left(x-5\right)^2+2\left(2x-1\right)\left(x-5\right)+\left(2x-1\right)^2-4\left(x-3\right)^2\)

\(=\left(x-5+2x-1\right)^2-\left(2x-6\right)^2\)

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

\(=\left[\left(3x-6\right)-\left(2x-6\right)\right].\left[\left(3x-6\right)+\left(2x-6\right)\right]\)

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

\(=\left(5x-12\right)x\)