Phân tích các đa thức sau thành phân tử:
a) \(125x^3+y^6\)
b) \(5xy^2-10xyz+5xz^2\)
c) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)
d) \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
e) \(100x^2-\left(x^2+25\right)^2\)
f) \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
a)ta co: 125x^3+y^6=(5x)^3+(y^2)^3=(5x+y^2)(5x-5xy^2+y^2) b)ta co 5xy^2-10xyz+5xz^2=5x(y^2-2yz+z^2)=5x(y-z)^2 (may cau sau gan giong ban tu lam nha)
b) \(5xy^2-10xyz+5xz^2\)
\(=5xy^2-5xyz-5xyz+5xz^2\)
\(=5xy\left(y-z\right)-5xz\left(y-z\right)\)
\(=\left(y-z\right)\left(5xy-5xz\right)\)
\(=5x\left(y-z\right)\left(y-z\right)\)
\(=5x\left(y-z\right)^2\)
c) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=\left(a+b+c\right)\left(\sqrt{3x}+6\sqrt{3y}\right)^2\)
d) \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4-8x\right)\)
\(=\left(4x-8\right)\left(x^2+6-x-7-9\right)\)
\(=4\left(x-2\right)\left(x^2-x-10\right)\)
\(=4\left(x-2\right)\left(x^2+x-10x-10\right)\)
\(=4\left(x-2\right)\left[x\left(x+1\right)-10\left(x+1\right)\right]\)
\(=4\left(x-2\right)\left(x+1\right)\left(x-10\right)\)
e) \(100x^2-\left(x^2+25\right)^2\)
\(=\left(10x-x^2-25\right)\left(10x+x^2+25\right)\)
\(=-\left(x^2-10x+25\right)\left(x^2+10x+25\right)\)
\(=-\left(x-5\right)^2\left(x+5\right)^2\)
