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a,15x^2-60=15x^2-15*4=15(x^2-4)
b,=(x^2+2xy+y^2)-25=(x+y)^2-5^2=[(x-y)+5][(x-y)-5]
xog 2 phần
1) \(4x^5y^2-8x^4y^2+4x^3y^2\)
\(=4x^3y^2\left(x^2-2x+1\right)\)
\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=4x^3y^2\left(x-1\right)^2\)
2) \(5x^4y^2-10x^3y^2+5x^2y^2\)
\(=5x^2y^2\left(x^2-2x+1\right)\)
\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=5x^2y^2\left(x-1\right)^2\)
3) \(12x^2-12xy+3y^2\)
\(=3\left(4x^2-4xy+y^2\right)\)
\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=3\left(2x-y\right)^2\)
4) \(8x^3-8x^2y+2xy^2\)
\(=2x\left(4x^2-4xy+y^2\right)\)
\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=2x\left(2x-y\right)^2\)
5) \(20x^4y^2-20x^3y^3+5x^2y^4\)
\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)
\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=5x^2y^2\left(2x-y\right)^2\)
1: 4x^5y^2-8x^4y^2+4x^3y^2
=4x^3y^2(x^2-2x+1)
=4x^3y^2(x-1)^2
2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)
3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)
4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)
5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)
a) \(4x^2-81=\left(2x\right)^2-9^2=\left(2x-9\right)\left(2x+9\right)\)
b) \(3\left(x-y\right)+5x\left(y-x\right)=3\left(x-y\right)-5x\left(x-y\right)=\left(x-y\right)\left(3-5x\right)\)
c) \(x\left(x+y\right)+6x+6y=x\left(x+y\right)+6\left(x+y\right)=\left(x+y\right)\left(x+6\right)\)
d) \(20x-5y=5\left(4x-y\right)\)
e) \(=2xy\left(5xy-4y+2y\right)\)
g) \(4xy+8xyz=4xy\left(1+2z\right)\)
1)
\(6x^2+12xy+6y^2\)
\(=6(x^2+2xy+y^2)=6[(x^2+xy)+(xy+y^2)]\)
\(=6[x(x+y)+y(x+y)]=6(x+y)^2\)
2)
\(-3x^4y^2-6x^3y^2-3x^2y^3\)
\(=-3x^2y^2(x^2+2x+y)\)
3) \(-3x^4y-12x^2y-12x^2y\)
\(=-3x^4y-24x^2y\)
\(=-3x^2y(x^2+8)\)
4)
\(5x^4y^2+20x^3y^2+20x^2y^2\)
\(=5x^2y^2(x^2+4x+4)\)
\(=5x^2y^2[x^2+2x+2x+4]\)
\(=5x^2y^2[x(x+2)+2(x+2)]=5x^2y^2(x+2)^2\)
5)
\(4x^5y^2-8x^4y^2+4x^3y^2\)
\(=4x^3y^2(x^2-2x+1)\)
\(=4x^3y^2(x^2-x-x+1)\)
\(=4x^3y^2[x(x-1)-(x-1)]=4x^3y^2(x-1)^2\)
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