a) 5x² - 5xy + 7y - 7x = ( 5x² - 5xy ) - ( 7x - 7y ) = 5x( x - y ) - 7( x - y ) = ( x - y )( 5x - 7 )

b) x² - y² + 2x + 1 = ( x² + 2x + 1 ) - y² = ( x + 1 )² - y² = ( x - y + 1 )( x + y + 1 )

c) 3x² + 6xy + 3y² - 3z² = 3( x² + 2xy + y² - z² ) = 3[ ( x² + 2xy + y² ) - z² ] = 3[ ( x + y )² - z² ] = 3( x + y - z )( x + y + z )

d) ab( x² + y² ) + xy( a² + b² ) = abx² + aby² + a²xy + b²xy

                                                = ( a²xy + abx² ) + ( aby² + b²xy )

                                                = ax( ay + bx ) + by( ay + bx )

                                                = ( ay + bx )( ax + by )

x² - x - y² - y

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

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

***

9x² + y² - 16z² + 6xy

= (3x + y)² - (4z)²

= (3x + y - 4z)(3x + y + 4z)

***

a³ - a²x - ay + xy

= a²(a - x) - y(a - x)

= (a - x)(a² - y)

***

2x² - 8y² + 3x + 6y

= 2(x² - 4y²) + 3(x + 2y)

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

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

***

xy(x + y) + yz(y + z) + xz(x + z) + 2xyz

= xy(x + y + z) + yz(x + y + z) + xz(x + z)

= y(x + y + z)(x + z) + xz(x + z)

= (x + z)(xy + y² + yz + xz)

= (x + z)[y(x + y) + z(x + y)]

= (x + z)(x + y)(y + z) 

a) x² ( x+ 2y) -x -2y

= x² ( x+ 2y) -(x+2y)

= (x²-1)(x+2y)

= (x-1)(x+1)(x+2y)

b)3x²- 3y² -2 (x-y)²

= 3(x²-y²) -2 (x-y)²

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

\(=\left(x-y\right)\left[3\left(x+y\right)-2\left(x-y\right)\right]\\ =\left(x-y\right)\left(3x+3y-2x+2y\right)\\ =\left(x-y\right)\left(x+5y\right)\)

c) x²- 2x-4y² - 4y

= (x²-4y²)-(2x+4y)

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

d) x³ - 4x² - 9x +36

= (x³+3x²)-(7x²+21x)+(12x+36)

= x²(x+3)-7x(x+3)+12(x+3)

=(x²-7x+12)(x+3)

\(=\left[\left(x^2-3x\right)-\left(4x-12\right)\right]\left(x+3\right)\\ =\left[x\left(x-3\right)-4\left(x-3\right)\right]\left(x+3\right)=\left(x-4\right)\left(x-3\right)\left(x+3\right)\)

a) = x² ( x+ 2y) -(x+2y)

= (x²-1)(x+2y)

= (x-1)(x+1)(x+2y)

b)= 3(x²-y²) -2 (x-y)²

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

=(x−y)[3(x+y)−2(x−y)]

=(x−y)(3x+3y−2x+2y)

=(x−y)(x+5y)

=(x−y)[3(x+y)−2(x−y)]

=(x−y)(3x+3y−2x+2y)

=(x−y)(x+5y)

c)= (x²-4y²)-(2x+4y)

=(x−2y)(x+2y)−2(x+2y)

=(x+2y)(x−2y−2)

=(x−2y)(x+2y)−2(x+2y)

=(x+2y)(x−2y−2)

d)= (x³+3x²)-(7x²+21x)+(12x+36)

= x²(x+3)-7x(x+3)+12(x+3)

=(x²-7x+12)(x+3)

=[(x2−3x)−(4x−12)](x+3)

=[x(x−3)−4(x−3)](x+3)

=(x−4)(x−3)(x+3)

a: \(x^2\left(x+2y\right)-x-2y\)

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

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

b: \(3x^2-3y^2-2\left(x-y\right)^2\)

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

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

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

c: Ta có: \(x^2-2x-4y^2-4y\)

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

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

d: Ta có: \(x^3-4x^2-9x+36\)

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

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

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

`a, x^3 + 4x = x(x^2+4)`

`b, 6ab - 9ab^2 = 3ab(2-b)`

`c, 2a(x-1) + 3b(1-x)`

`= (2a-3b)(x-1)`

`d, (x-y)^2 - x(y-x)`

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

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

Bài giải:

a) 3x - 6y = 3 . x - 3 . 2y = 3(x - 2y)

b) $\frac{2}{5}$x² + 5x³ + x²y = x² ($\frac{2}{5}$ + 5x + y)

c) 14x²y – 21xy² + 28x²y² = 7xy . 2x - 7xy . 3y + 7xy . 4xy = 7xy(2x - 3y + 4xy)

d) $\frac{2}{5}$x(y - 1) - $\frac{2}{5}$y(y - 1) = $\frac{2}{5}$(y - 1)(x - y)

e) 10x(x - y) - 8y(y - x) =10x(x - y) - 8y[-(x - y)]

= 10x(x - y) + 8y(x - y)

= 2(x - y)(5x + 4y)

a,\(3x-6y=3\left(x-2y\right)\)

b,\(x^2(\dfrac{2}{5}+5x+y)\)

c,\(7xy\left(2x-3y+4xy\right)\)

d,\(\dfrac{2}{5}x\left(y-1\right)-\dfrac{2}{5}y\left(y-1\right)\)

=\(\dfrac{2}{5}\left(y-1\right)\left(x-y\right)\)

e,\(10x\left(x-y\right)-8y\left(y-x\right)=10x\left(x-y\right)+8y\left(x-y\right)\)

\(2\left(x-y\right)\left(5x+4y\right)\)

Câu hỏi của nguyễn khánh linh - Toán lớp 8 - Học toán với OnlineMath

a: \(x^4+25x^2+20x-4\)

\(=x^4-5x^3+2x^2+5x^3-25x^2+10x-2x^2+10x-4\)

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

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

b: \(=x^4-6x^2-x^2+9\)

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

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

c: \(=abx^2+aby^2-a^2xy-b^2xy\)

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

\(=xb\left(ax-by\right)+ay\left(by-ax\right)\)

\(=\left(ax-by\right)\cdot\left(xb-ay\right)\)

\(a,3x-6y=3\left(x-2y\right)\)

\(b,\frac{2}{5}x^2+5x^3+x^2y=x^2\left(\frac{2}{5}+5x+y\right)\)

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

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

`c, (x+y)^2 - 2(x+y)z + z^2`

`= (x+y-z)^2`