1. 

\(\left(12x^2+6x\right)\left(y+z\right)+\left(12x^2+6x\right)\left(y-z\right)\\ =\left(12x^2+6x\right)\left(y+z+y-z\right)\\ =2y\left(12x^2+6x\right)\\ =2y.6x\left(2x+1\right)\\ =12xy\left(2x+1\right)\)

2. 

\(x\left(x-6\right)+10\left(x-6\right)=0\\ \Leftrightarrow\left(x-6\right)\left(x+10\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)

Vậy \(x\in\left\{6;-10\right\}\) là nghiệm của pt

Bài 1:

Ta có: \(\left(12x^2+6x\right)\left(y+z\right)+\left(12x^2+6x\right)\left(y-z\right)\)

\(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)

\(=6x\left(2x+1\right)\cdot2y\)

\(=12xy\left(2x+1\right)\)

Bài 2: 

Ta có: \(x\left(x-6\right)+10\left(x-6\right)=0\)

\(\Leftrightarrow\left(x-6\right)\left(x+10\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)

d) x^6 + y^6 = (x^2)^3 + (y^2)^3 

= (x^2 + y^2)(X^2 - x^2.y^2 + y^2)

c) = (x+y)^3 + 3(x+y)^2z + 3((x+y)z^2 + z^3 - X^3 - Y^3 - z^3

= (x+y)^3 + 3(x+y)^2z + 3((x+y)z^2  - (x+y)(x^2 - xy + y^2)

= (x+y)[(x+y)^2 + 3(x+y)z + 3z^2 - x^2 + xy - y^2]

= (X+y)(x^2 + 2xy + y^2 + 3xz + 3yz + 3z^2 - x^2 + xy - y^2)

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

= (x+y)[3x(y+z) + 3z(y+z)]

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

Đúng thì  

= 

b: \(=\dfrac{12\left(y-z\right)^4+3\left(y-z\right)^5}{6\left(y-z\right)^2}=2\left(y-z\right)^2+\dfrac{1}{2}\left(y-z\right)^3\)

\(x^6-y^6\)

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

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

x^{6 -} y⁶

= ( x³ )² - ( y³ ) ²

⁼ ( x³ + y³) ( x³ - y³ )

= ( x - y ) ( x² + xy + y^{2 )}.( x + y ) ( x² - xy + y^{2 )}

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

\(x^6-y^6\)

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

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

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

x⁶-y⁶ =(x-y)(x⁵+x⁴y+x³y²+x²y³+xy⁴+y⁵)