Question

Answer 1

mấy bro giúp em vs ạ

 

Answer 2

1) \(2x^2+5x^3+x^2y=x^2\left(2+5x+y\right)\)

2) \(3x^2-6xy+3y^2=3\left(x^2-2xy+y^2\right)=3\left(x-y\right)^2\)

3) \(3\left(x-y\right)-5y\left(y-x\right)=\left(3+5y\right)\left(x-y\right)\)

4) \(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)

5) \(\left(x+y\right)^3-\left(x-y\right)^3=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]=2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)=2y\left(3x^2+y^2\right)\)

6) \(3x^2-5x+2=3x^2-3x-2x+2=3x\left(x-1\right)-2\left(x-1\right)=\left(x-1\right)\left(3x-2\right)\)

7) \(x^2-3x+xy-3y=x\left(x-3\right)+y\left(x-3\right)=\left(x+y\right)\left(x-3\right)\)

8) \(x^2+y^2-2xy-25=\left(x-y\right)^2-5^2=\left(x-y-5\right)\left(x-y+5\right)\)

9) \(x^3-x+3x^2y+3xy^2+y^3-y=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)

 

Answer 3

10) \(x^4-2x^3+x^2-9=\left(x^4-x^3-3x^2\right)-x^3+4x^2-9=\left(x^4-x^3-3x^2\right)-x^3+x^2+3x+3x^2-3x-9=\left(x^4-x^3-3x^2\right)-\left(x^3-x^2-3x\right)-\left(3x^2-3x-9\right)=x^2\left(x^2-x-3\right)-x\left(x^2-x-3\right)-3\left(x^2-x-3\right)=\left(x^2-x-3\right)^2\)

11) \(4x^4+16=\left[4x^4+16x^2+16\right]-16x^2=\left(2x+4\right)^2-\left(4x\right)^2=\left(2x+4-4x\right)\left(2x+4+4x\right)=4\left(x-2x+2\right)\left(x+2x+2\right)\)