\(x^2+4x-9y^2+4\)

\(=\left(x^2+2.2x+2^2\right)-\left(3y\right)^2\)

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

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

\(x^2-9y^2-6y-1\)

\(=x^2-\left[\left(3y\right)^2+2.3y+1^2\right]\)

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

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

Tham khảo nhé~

a/Ta có:x²+4x-9y²+4

=x²+4x+4-(3y)²

=(x+2)²-(3y)²

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

b/Ta có:x²-9y²-6xy-1

=x²-6xy-(3y)²-1

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

a) = (4x² +4x + 1) - (9y² + 6y + 1) = (2x+ 1)² - (3y + 1)² = (2x+ 1+ 3y + 1).(2x + 1 - 3y - 1) = (2x+ 3y+ 2).(2x-3y)

b) = x² - 2015x + 2014x - 2014.2015 = x.(x - 2015) + 2014. (x - 2015) = (x + 2014).(x - 2015)

=4x^2+2xy-18xy-9y^2

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

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

4x^2+2xy-18xy-9y^2

=2x(2x+y)-9y(2x+y)

=(2x-9y)(2x+y)

Sorry bài trên mình làm sai 

a: =x^2+5x-x-5

=(x+5)(x-1)

b: =4x^2-(y-3)^2

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

1. x² + x - y² +y 

= (x²  -y²) + (x+y)

= (x-y)(x+y) + (x+y)

= (x+y)(x-y+1)

2. 4x² - 9y² + 4x -6y

= (2x)² -(3y)² + 2(2x - 3y)

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

= (2x-3y)(2x+3y+2) 

3. x² - 9 - 5x - 15 

= x² - 5x - 24

= x² - 8x + 3x -24

= x(x-8) + 3(x-8)

= (x-8)(x+3)

a: \(ab+a+b+1\)

\(=a\left(b+1\right)+\left(b+1\right)\)

\(=\left(b+1\right)\left(a+1\right)\)

c: \(4x^2-12xy+3x-9y\)

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

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

    4x² + 4x - 9y² + 1

= (4x² + 4x + 1) - 9y²

= (2x + 1)² - 9y²

^{=  (2x + 1 - 3y)(2x + 1 + 3y)}

4x² - 11xy + 6y²

= 4x² - 8xy - 3xy + 6y²

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

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