Bài 4:
1: \(5x^2+x=0\)
=>x(5x+1)=0
=>\(\left[\begin{array}{l}x=0\\ 5x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-\frac15\end{array}\right.\)
2: \(x^2-7x=0\)
=>x(x-7)=0
=>\(\left[\begin{array}{l}x=0\\ x-7=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=7\end{array}\right.\)
3: \(3x^2-6x=0\)
=>3x(x-2)=0
=>x(x-2)=0
=>\(\left[\begin{array}{l}x=0\\ x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=2\end{array}\right.\)
4: \(x^2+7x=0\)
=>x(x+7)=0
=>\(\left[\begin{array}{l}x=0\\ x+7=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-7\end{array}\right.\)
5: \(7x^2+2x=0\)
=>x(7x+2)=0
=>\(\left[\begin{array}{l}x=0\\ 7x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-\frac27\end{array}\right.\)
6: \(x^2+6x=0\)
=>x(x+6)=0
=>\(\left[\begin{array}{l}x=0\\ x+6=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-6\end{array}\right.\)
Bài 3:
1: \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)
2: \(x^2-16y^2=x^2-\left(4y\right)^2=\left(x-4y\right)\left(x+4y\right)\)
3: \(9x^2-1=\left(3x\right)^2-1^2=\left(3x-1\right)\left(3x+1\right)\)
1: \(\left(3x+1\right)^2-\left(x+1\right)^2\)
=(3x+1-x-1)(3x+1+x+1)
=2x(4x+2)
=4x(2x+1)
2: \(\left(x+y\right)^2-\left(x-y\right)^2\)
=(x+y+x-y)(x+y-x+y)
\(=2x\cdot2y=4xy\)
3: \(\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left(2xy+1+2x+y\right)\left(2xy+1-2x-y\right)\)
=[2x(y+1)+(y+1)][2x(y-1)-(y-1)]
=(2x+1)(y+1)(2x-1)(y-1)
Bài 2:
1: 2y(x+2)-3x-6
=2y(x+2)-3(x+2)
=(x+2)(2y-3)
2: \(3\left(x+4\right)-x^2-4x\)
=3(x+4)-x(x+4)
=(x+4)(3-x)
3: \(2\left(x+5\right)-x^2-5x\)
=2(x+5)-x(x+5)
=(x+5)(2-x)
4: x(x+y)-7x-7y
=x(x+y)-7(x+y)
=(x+y)(x-7)
5: \(x^2\left(x-y\right)+2x-2y\)
\(=x^2\left(x-y\right)+2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+2\right)\)
6: x(x+3y)-5x-15y
=x(x+3y)-5(x+3y)
=(x+3y)(x-5)
Bài 1:
1: 3x-3y=3(x-y)
2: 10x+15y=5(2x+3y)
3: 3x-12y
\(=3\cdot x-3\cdot4y\)
=3(x-4y)
4: \(4x-20=4\cdot x-4\cdot5=4\left(x-5\right)\)
5: \(6x-2x^2=2x\cdot3-2x\cdot x=2x\left(3-x\right)\)
6: \(2x-4x^2=2x\cdot1-2x\cdot2x=2x\left(1-2x\right)\)
7: \(3x^2-6x=3x\cdot x-3x\cdot2=3x\left(x-2\right)\)
8: \(3x^2+6x=3x\cdot x+3x\cdot2=3x\left(x+2\right)\)
