bạn tách ra từng ít câu 1 thôi ạ

a: \(=5x\left(xy^2+3x+6y^2\right)\)

b: \(=\left(x-2\right)\left(x+3\right)-\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(x+3-x-2\right)=\left(x-2\right)\)

c: \(=\left(x-3\right)\left(x-4\right)\)

d: \(=x\left(x^2-2xy+y^2-9\right)\)

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

e: \(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)

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

a) (x - 1)(x - 2).                        b) 4(x - 2)(x - 7).

c) (x + 2)(2x +1).                    d) (x - l)(2x - 7).

e) (2x + 3y - 3)(2x - 3y +1).    g) (x - 3)( x 3   +   x 2  - x +1).

h) (x + y)(x + y-l)(x + y + l).

chịu

a) \(3x\left(2x-y\right)+5y\left(y-2x\right)\)

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

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

b) \(\left(x-5\right)^2-9\left(x+y\right)^2\)

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

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

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

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

a: \(3x\left(2x-y\right)+5y\left(y-2x\right)=\left(2x-y\right)\left(3x-5y\right)\)

e: \(x^2-10x+24=\left(x-4\right)\left(x-6\right)\)

g) \(6x^2+7x-5\)

=\(6x^2+10x-3x-5\)

=\(\left(6x^2+10x\right)-\left(3x+5\right)\)

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

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

a) (x + y)² - 2(x + y) + 1 

= (x + y)² - 2.1.(x + y) + 1

= (x + y - 1)²

b) x³ + 1 - x² - x

= (x³ - x²) - (x - 1) 

= x²(x - 1) - (x - 1)

= (x² - 1)(x - 1) = (x - 1)(x + 1)(x - 1) = (x - 1)²(x + 1) 

c) 27x³ - 0,001 

= \(\left(3x\right)^3-\frac{1}{1000}=\left(3x\right)^3-\left(\frac{1}{10}\right)^3=\left(3x-\frac{1}{10}\right)\left(9x^2+\frac{3}{10}x+\frac{1}{100}\right)\)

d) 125x³ - 1 =(5x)³ - 1 = (5x - 1)(25x² + 5x + 1) 

e) (x² + 4)² - 16x² 

= (x² + 4)² - (4x)²

= (x² - 4x + 4)(x² + 4x + 4) 

= (x - 2)²(x + 2)²

= [(x - 2)(x + 2)]²

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

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

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

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

b.\(x^3+1-x^2-x\)

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

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

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

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

c.\(27x^3-0,001\)

\(=27x^3-\frac{1}{1000}\)

\(=\left(3x\right)^3-\left(\frac{1}{10}\right)^3\)

\(=\left(3x-\frac{1}{10}\right)\left(9x^2+0,3x+\frac{1}{100}\right)\)

d,\(125x^3-1\)

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

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

e.\(\left(x^2+4\right)^2-16x^2\)

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

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

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

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

x 2 y + x y 2  +  x 2 z + x z 2  +  y 2 z + y z 2  + 3xyz.

= ( x 2  y +  x 2 z + xyz) + (x y 2  +  y 2 z + xyz) + (x z 2  + y z 2  + xyz)

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

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

\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+x^2z+xyz\right)+\left(xz^2+yz^2+xyz\right)+\left(xy^2+y^2z+xyz\right)\)

\(=x\left(xy+xz+yz\right)+z\left(xz+yz+xy\right)+y\left(xy+yz+xz\right)\)

\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)

1. Ta có: hằng đẳng thức: \(x^3+y^3+z^3=3xyz\) nếu x+y+z=0

đặt b-c=x, c-a=y, a-b=z⇒x+y+z=0

 \(\Rightarrow\left(b-c\right)^3+\left(c-a\right)^3+\left(a-b\right)^3=3\left(a-b\right)\left(c-a\right)\left(b-c\right)\)

2. \(x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

3. Tham khảo: https://hoc247.net/hoi-dap/toan-8/phan-tich-da-thuc-x-y-5-x-5-y-5-thanh-nhan-tu-faq447273.html

\(5,=x^3+2x^2y-7x^2y-14xy^2\\ =x^2\left(x+2y\right)-7xy\left(x+2y\right)\\ =x\left(x-7y\right)\left(x+2y\right)\)