Câu 1:
a: \(5x^2\left(5x^2-2x+1\right)\)
\(=5x^2\cdot5x^2-5x^2\cdot2x+5x^2\cdot1\)
\(=25x^4-10x^3+5x^2\)
b: \(\left(5x-2y\right)\left(x^2-xy+1\right)\)
\(=5x^3-5x^2y+5x-2x^2y+2xy^2-2y\)
\(=5x^3-7x^2y+5x+2xy^2-2y\)
c: \(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)
\(=2x^3-3x-5x^3-x^2+x^2=-3x^3-3x\)
d: \(\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)-\left(2x^2+1\right)^2\)
\(=\left(2x^2+1\right)^2-4x^2-\left(2x^2+1\right)^2\)
\(=-4x^2\)
Câu 2:
a: \(5x^2+3x^4=x^2\cdot5+x^2\cdot3x^2=x^2\left(3x^2+5\right)\)
b: \(64x^3-125y^3=\left(4x\right)^3-\left(5y\right)^3\)
\(=\left(4x-5y\right)\left\lbrack\left(4x\right)^2+4x\cdot5y+\left(5y\right)^2\right\rbrack\)
\(=\left(4x-5y\right)\left(16x^2+20xy+25y^2\right)\)
c: \(x^2-2xy+y^2-3x\left(x-y\right)\)
\(=\left(x-y\right)^2-3x\left(x-y\right)\)
=(x-y)(x-y-3x)
=(x-y)(-2x-y)
Câu 3:
a: 7-5x=0
=>5x=7
=>\(x=\frac75\)
b: x(x+2)-3x-6=0
=>x(x+2)-3(x+2)=0
=>(x+2)(x-3)=0
=>\(\left[\begin{array}{l}x+2=0\\ x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-2\\ x=3\end{array}\right.\)
c: \(x+2=\left(x+2\right)^2\)
=>\(\left(x+2\right)\left(x+2-1\right)=0\)
=>(x+2)(x+1)=0
=>\(\left[\begin{array}{l}x+2=0\\ x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-2\\ x=-1\end{array}\right.\)
