Question

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Answer 1

[Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )]

a) \(5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)\)

\(=5\left[\left(x-y\right)^2-4z^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\)

b) \(x^2-z^2+y^2-2xy=\left(x^2-2xy+y^2\right)-z^2\)

\(=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

c) \(a^3-ay-a^2x+xy=a^2\left(a-y\right)-x\left(a^2-y\right)=\left(a^2-x\right)\left(a^2-y\right)\)

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

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

Answer 2

[Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )]

e) \(3x^2-6xy+3y^2-12z^2=3\left(x^2-2xy+y^2-4z^2\right)\)

\(=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)

f) \(x^2-6xy+9y^2-25z^2=\left(x-3y\right)^2-25z^2=\left(x-3y-5z\right)\left(x-3y+5z\right)\)

g) \(x^2-y^2+2yz-z^2=x^2-\left(y^2-2yz+z^2\right)\)

\(=x^2-\left(y-z\right)^2=\left(x-y+z\right)\left(x+y-z\right)\)