Đáp án:

 1)
a,b,c,d,e,f Đúng
$2)
a)A=-8\\
b)  B(1)=8\\
\Rightarrow B(-1)=0\\
c)
C=1\\
e) E=\dfrac{-1}{2}\\
f) F(-2)=-7\\
3)
a)
x=\dfrac{15}{2}\\
b) (2x-3)^2-x(2x-3)=0\\
 {\left[\begin{aligned}x=\dfrac{3}{2}\\x=3\end{aligned}\right.}\\
c) 9x^2-4=x(3x-2)\\
 {\left[\begin{aligned}x=\dfrac{2}{3}\\x=-1\end{aligned}\right.}\\
d) 4x^2-25-x(2x-5)=0\\
 {\left[\begin{aligned}x=\dfrac{5}{2}\\x=-5\end{aligned}\right.}\\$

Giải thích các bước giải:

 $1)
a) (a+b)^2+(a-b)^2=a^2+2ab+b^2+a^2-2ab+b^2=2(a^2+b^2)\Rightarrow Đ\\
b) (a+b)^2-(a-b)^2=a^2+2ab+b^2-a^2+2ab-b^2=4ab\Rightarrow Đ\\
c) a^3+b^3=(a+b)^3-3a^2b-3ab^2=(a+b)^2-3a(a+b)\Rightarrow Đ\\
d) a^3-b^3=(a-b)^3+3a^2b-3ab^2=(a+b)^2+3ab(a-b)\Rightarrow Đ\\
e)(a+b+c)^2=(a+b)^2+c^2+2(a+b).c=a^2+2ab+b^2+c^2+2ac+2bc\Rightarrow Đ\\
f) (a+b-c)^2=(a+b)^2+c^2-2(a+b)c=a^2+2ab+b^2+c^2-2ac-2bc\Rightarrow Đ\\
2)
a)A=x^3-3x^2+3x-1=(x-1)^3\\
\Rightarrow A(-1)=(-1-1)^3=(-2)^3=-8\\
b) \left | x \right |=1\rightarrow x=\pm 1\\
B=x^3+3x^2+3x+1=(x+1)^3\\
\Rightarrow B(1)=(1+1)^3=2^3=8\\
\Rightarrow B(-1)=(-1+1)^3=0\\
c)
C=x^3+3x^2+12x+8=(x+2)^3\\
\Rightarrow C(-3)=(-3+2)^3=(-1)^3=-1\\
d)D=x^3-3x^2+12x-8=(x-2)^3\\
\Rightarrow D(3)=(3-2)^3=1\\
e) E=(x-1)(x^2+x+1)-x(x^2+1)\\
=x^3-1-x^3+x=x-1\\
\Rightarrow E(\dfrac{1}{2})=\dfrac{1}{2}-1=\dfrac{-1}{2}\\
f)F=(x+1)(x^2-x+1)+x(3-x^2)\\
=x^3-1+3x-x^3=3x-1\\
\Rightarrow F(-2)=3.(-2)-1=-7\\
3)
a)
(2x+1)^2+(3x-1)^2=13.(x+1).(x-1)\\
\Leftrightarrow 4x^2+4x+1+9x^2-6x+1=13(x^2-1)\\
\Leftrightarrow 13x^2-2x+2-13x^2+13=0\\
\Leftrightarrow -2x+15=0\\
\Leftrightarrow 2x=15\\
\Leftrightarrow x=\dfrac{15}{2}\\
b) (2x-3)^2-x(2x-3)=0\\
\Leftrightarrow (2x-3)(2x-3-x)=0\\
\Leftrightarrow (2x-3)(x-3)=0\\
\Leftrightarrow {\left[\begin{aligned}2x-3=0\\x-3=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{3}{2}\\x=3\end{aligned}\right.}\\
c) 9x^2-4=x(3x-2)\\
\Leftrightarrow 9x^2-4-3x^2+2x=0\\
\Leftrightarrow 6x^2+2x-4=0\\
\Leftrightarrow 3x^2+x-2=0\\
\Leftrightarrow 3x^2+3x-2x-2=0\\
\Leftrightarrow 3x(x+1)-2(x+1)=0\\
\Leftrightarrow (3x-2)(x+1)=0\\
\Leftrightarrow {\left[\begin{aligned}3x-2=0\\x+1=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{2}{3}\\x=-1\end{aligned}\right.}\\
d) 4x^2-25-x(2x-5)=0\\
\Leftrightarrow 4x^2-25-2x^2+5x=0\\
\Leftrightarrow 2x^2+5x-25=0\\
\Leftrightarrow 2x^2+10x-5x-25=0\\
\Leftrightarrow 2x(x+5)-5(x+5)=0\\
\Leftrightarrow (2x-5)(x+5)=0\\
\Leftrightarrow {\left[\begin{aligned}2x-5=0\\x+5=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{5}{2}\\x=-5\end{aligned}\right.}\\$