Bài 1:
a: \(81-25x^2-10xy-y^2\)
\(=81-\left(25x^2+10xy+y^2\right)\)
\(=81-\left(5x+y\right)^2=\left(9-5x-y\right)\left(9+5x+y\right)\)
b: \(\left(7x-4\right)^2-\left(2x+1\right)^2\)
\(=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)\)
\(=15\left(x-1\right)\left(3x-1\right)\)
Bài 2:
a: \(\left(3x-1\right)^2=\left(x+2\right)^2\)
=>\(\left(3x-1-x-2\right)\left(3x-1+x+2\right)=0\)
=>(2x-3)(4x+1)=0
=>\(\left[{}\begin{matrix}2x-3=0\\4x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
b: x(x+6)-7x-42=0
=>x(x+6)-7(x+6)=0
=>(x+6)(x-7)=0
=>\(\left[{}\begin{matrix}x+6=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
....
Bài 1 :
c) x^2y + xy^2 + x^2z + xz^2+y^2z + yz ^2+ 3xyz
= \(\)\(\)( x^2y + x^2z + xyz) + ( xy^2 + y^2z +xyz) + (xz^2+ yz^2 + xyz)
= x( xy+ xz + yz) + y(xy+ yz + xz) + z(xz + yz + xy)
= ( xy+ xz+yz ) .( x+y+z)
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