a) 4x² + 12xy² = 4x.(x+3y²)

b) 3x³y² - 9x²y² +15x²y = 3x²y.(xy - 3y +5)

c) 10x.(x-y) + 5y.(x-y) = 5.(x-y).(2x+y)

d) x² + 4xy - 16 + 4y²

= (x+2y)² - 16

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

e) 3x² + 5y - 3xy - 5x

= 3x.(x-y) - 5.(x-y)

= (x-y).(3x-5)

g) 5x² -10xy + 5y² - 20z²

= 5.(x² -2xy + y² - 4z² )

= 5.[ (x-y)² - 4z² ]

= 5.(x-y-4z).(x-y+4z)

câu h đề giống câu d nha bn

F(x) = ( x^50 + x^49 + ....+ x^34) + ( x^33 + x^ 32 +...+ x^17) + ( x^16 + x^15+...+ 1)

= x^34 ( x^16 + x^15 +...+1) +x^17( x^16 + x^15+...+ 1) + (x^16+...+1)

=(x^16 + ....+ 1)(x^34 + x^17+ 1)    chia hết cho ( x^16 + x^15 + ...+1)

Hay F(x) chia het cho G(x)

x² - 2x + 4 - x² - 9 = 6

- 2x - 5 = 6

-2x = 11

x= \(-\frac{11}{2}\)

(x-2)²-(x-3)(x+3)=6

x²-4x+4-(x²-9)=6

x²-4x+4-x²+9=6

-4x+13=6

-4x=6-13

-4x=-7

x=(-7):(-4)

x=7/4

\(\left(2x-1\right)\left(x-5\right)-x^2+10x-25=0\)

\(\left(2x-1\right)\left(x-5\right)-\left(x^2-10x+25\right)=0\)

\(\left(2x-1\right)\left(x-5\right)-\left(x-5\right)^2=0\)

\(\left(x-5\right)\left(2x-1-x+5\right)=0\)

\(\left(x-5\right)\left(x+4\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-5=0\\x+4=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=5\\x=-4\end{cases}}\)

Vậy \(\orbr{\begin{cases}x=5\\x=-4\end{cases}}\)

\(\left(5n-3\right)^2-9=\left(5n-3\right)^2-3^2=\left(5n-3-3\right)\left(5n-3+3\right)=5n\left(5n-6\right)\)

Ta có: \(5⋮5\)

\(\Rightarrow5n\left(5n-6\right)⋮5\forall n\in Z\)

\(\Rightarrow\left(5n-3\right)^2-9⋮5\forall n\in Z\)

                                  đpcm