Đáp án:
$1) a) (3x-6)(3x+6)\\
b)2xy.(x-y)^2\\
c) (a-b)(b-a)\\
2)
a) x^4-(x-3)^2\
b) 3x^2-5x+2\\
3)
{\left[\begin{aligned}x=0\\x=3\\ x=-3\end{aligned}\right.}\\$
Giải thích các bước giải:
$1) a) 9x^2-36=(3x)^2-6^2=(3x-6)(3x+6)\\
b) 2x^3y-4x^2y^2+2xy^2=2xy(x^2-2xy+y^2)=2xy.(x-y)^2\\
c) ab-b^2-a+b=b(a-b)-(a-b)=(a-b)(b-a)\\
2)
a) (x^2+x-3)(x^2-x+3)=(x^2)^2-(x-3)^2=x^4-(x-3)^2\
b) (6x^3-7x^2-x+2):(2x+1)\\
=\left ( 6x^3+3x^2-10x^2-5x+4x+2 \right ):(2x+1)\\
=\left [ 3x^2(2x+1)-5x(2x+1)+2(2x+1) \right ]:(2x+1)\\
=\left [ (2x+1)(3x^2-5x+2) \right ]:(2x+1)\\
=3x^2-5x+2\\
3)
(x-1)^3+3x(x-4)+1=0\\
\Leftrightarrow x^3-3x^2+3x-1+3x^2-12x+1=0\\
\Leftrightarrow x^3-9x=0\\
\Leftrightarrow x(x^2-9)=0\\
\Leftrightarrow x(x-3)(x+3)=0
\Leftrightarrow {\left[\begin{aligned}x=0\\x-3=0\\ x+3=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=3\\ x=-3\end{aligned}\right.}\\$
