\(\left(2x^2-y\right)\left(4x^2-5xy^2+3y^2\right)\)
\(=\left(2x^2-y\right)4x^2-\left(2x^2-y\right)5xy^2+\left(2x^2-y\right)3y^2\)
\(=8x^4-4x^2y-10x^3y^2+5xy^3+6x^2y^2-3y^3\)
\(\text{Câu 1: }\left(2x^2-y\right)\left(4x^2-5xy^2+3y^2\right)\\ \\=2x^2\left(4x^2-5xy^2+3y^2\right)-y\left(4x^2-5xy^2+3y^2\right)\\ \\=\\8x^4-10x^3y^2+6x^2y^2-4x^2y+5xy^3+3y^3\)
Câu 2:
\(\text{ a) }48x^2y^2-3y^2+6xy-3x^2\\ \\ =3\left(16x^2y^2-y^2+2xy-x^2\right)\\ \\ =3\left[16x^2y^2-\left(x^2-2xy+y^2\right)\right]\\ =3\left[\left(4xy\right)^2-\left(x-y\right)^2\right]\\ \\ =3\left(4xy-x+y\right)\left(4xy+x-y\right)\)
\(\text{b) }2x^3y-4x^2y^2+2xy^3\\ \\=2xy\left(x^2-2xy+y^2\right)\\ \\=2xy\left(x-y\right)^2\)
\(\text{c) }4x^2-6x^3y-2x^2+8x\\ \\=2x^2-6x^3y+8x\\ \\ =2x\left(x-3x^2y+4\right)\)
\(\text{d) }6xy+5x-5y-3x^2-3y^2\\ \\ =\left(5x-5y\right)-\left(3x^2-6xy+3y^2\right)\\ \\ =5\left(x-y\right)-3\left(x^2-2xy+y^2\right)\\ \\ =5\left(x-y\right)-3\left(x-y\right)^2\\ \\ =\left(x-y\right)\left[5-3\left(x-y\right)\right]\\ =\left(x-y\right)\left(5-3x+3y\right)\)
\(a,48x^2y^2-3y^2+6xy-3x^2=3\left(16x^2y^2-y^2+2xy-x^2\right)=3\left[\left(4xy\right)^2-\left(y^2-2xy+x^2\right)\right]=3\left[\left(4xy\right)^2-\left(y-x\right)^2\right]=3\left(4xy-y+x\right)\left(4xy+y-x\right)\)
\(b,2x^3y-4x^2y^2+2xy^3=2xy\left(x^2-2xy+y^2\right)=2xy\left(x-y\right)^2\)
b) \(2x^3y-4x^2y^2+2xy^3\)
\(=2xy\left(x^2-2xy+y^2\right)\)
\(=2xy\left(x-y\right)^2\)
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