Mn giúp mình vs nha •---•

Đáp án:

 $3)
a) -(x-3y)^2\\
b)
34x^2-5y^2-12xy\\
c)
x^3-8x^2+9x-3\\
4)
a)
x=\dfrac{5}{6}\\
b)
 x=\dfrac{-35}{4}\\
5)
a) x=\pm 5\\
d)
 {\left[\begin{aligned}x=2\\x=-4\end{aligned}\right.}\\
6)
a) x10000\\
b)8100$

Giải thích các bước giải:

 $3)
a) (5x-2y)(3x+4y)-(4x+y)^2\\
=15x^2+20xy-6xy-8y^2-(16x^2+8xy+y^2)\\
=15x^2+20xy-6xy-8y^2-16x^2-8xy-y^2\\
=(15x^2-16x^2)+(20xy-6xy-8xy)+(-8y^2-y^2)\\
=-x^2+6xy-9y^2\\
=-(x^2-6xy+9y^2)\\
=-(x-3y)^2\\
b)
(3x-2y)^2+(5x-3y)(3y+5x)\\
=(3x)^2-2.3x.2y+(2y)^2+(5x)^2-(3y)^2\\
=9x^2-12xy+4y^2+25x^2-9y^2\\
=(9x^2+25x^2)+(4y^2-9y^2)-12xy\\
=34x^2-5y^2-12xy\\
c)
(x^2-3x+2)(x-1)-(2x-1)^2\\
=x^3-x^2-3x^2+3x+2x-2-(4x^2-4x+1)\\
=x^3-x^2-3x^2+3x+2x-2-4x^2+4x-1\\
=x^3+(-x^2-3x^2-4x^2)+(3x+2x+4x)+(-2-1)\\
=x^3-8x^2+9x-3\\
4)
a)
(x-3)^2-(x+1)(x-1)=5\\
\Leftrightarrow x^2-6x+9-(x^2-1)=5\\
\Leftrightarrow x^2-6x+9-x^2+1=5\\
\Leftrightarrow (x^2-x^2)-6x+(9+1)-5=0\\
\Leftrightarrow -6x+5=0\\
\Leftrightarrow x=\dfrac{5}{6}\\
b)
(2x-5)(5+2x)-(2x+1)^2=9\\
\Leftrightarrow (2x)^2-5^2-(4x^2+4x+1)=9\\
\Leftrightarrow 4x^2-25-4x^2-4x-1=9\\
\Leftrightarrow (4x^2-4x^2)-4x+(-25-1)=9\\
\Leftrightarrow -4x-26=9\\
\Leftrightarrow -4x=35\\
\Leftrightarrow x=\dfrac{-35}{4}\\
5)
a) x^2=25\Leftrightarrow x=\pm \sqrt{25}=\pm 5\\
d)
x^2+2x+1=9\Leftrightarrow (x+1)^2=9\Leftrightarrow x+1=\pm 3\\
\Leftrightarrow {\left[\begin{aligned}x=2\\x=-4\end{aligned}\right.}\\
6)
a) x^2+2xy+y^2=(x+y)^2\Rightarrow (73+27)^2=100^2=10000\\
b)m^2-4m+4=(m-2)^2\Rightarrow (92-2)^2=90^2=8100$