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\(5x^4y+10x^3y+10x^2y^3+5xy^4\)
\(=5xy.x^3+5xy.2x^3+5xy.2xy^3+5xy.y^3\)
\(=5xy\left(x^3+2x^3+2xy^3+y^3\right)\)
Ht pt
a: \(=5xy\left(x^2-2xy+y^2\right)=5xy\left(x-y\right)^2\)
b: \(=2x^2+10x-3x-15\)
\(=2x\left(x+5\right)-3\left(x+5\right)=\left(x+5\right)\left(2x-3\right)\)
\(\left(x+y\right)^2+3\left(x+y\right)-10=\left[\left(x+y\right)^2+2\left(x+y\right).\dfrac{3}{2}+\dfrac{9}{4}\right]-\dfrac{49}{4}\)
\(=\left(x+y+\dfrac{3}{2}\right)^2-\dfrac{49}{4}=\left(x+y+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x+y+\dfrac{3}{2}+\dfrac{7}{2}\right)=\left(x+y-2\right)\left(x+y+5\right)\)
\(\left(x+y\right)^2+3\left(x+y\right)-10\)
\(=\left(x+y\right)^2+5\left(x+y\right)-2\left(x+y\right)-10\)
\(=\left(x+y+5\right)\left(x+y-2\right)\)
\(=2\left(x^2-y^2\right)-6\left(x+y\right)=2\left(x-y\right)\left(x+y\right)-6\left(x+y\right)=\left(x+y\right)\left(2x-2y-6\right)\) Đảm bảo chuẩn ko cần chỉnh (•••
check mk nhá
\(\left(x+y+z\right)^2+\left(x+y-z\right)^2-4z^2=\left(x+y+z\right)^2+\left(x+y-z-2z\right)\left(x+y-z+2z\right)=\left(x+y+z\right)^2+\left(x+y-3z\right)\left(x+y+z\right)=\left(x+y+z\right)\left(x+y+z+x+y-3z\right)=\left(x+y+z\right)\left(2x+2y-2z\right)=2\left(x+y+z\right)\left(x+y-z\right)\)
Ta có:
(x + y + z)2 + (x + y – z)2 – 4z2
\(=\left(x+y-z\right)^2+\left(x+y-z\right)\left(x+y+3z\right)\)
\(=\left(x+y-z\right)\left(x+y+3z+x+y-z\right)\)
\(=2\left(x+y-z\right)\left(x+y+z\right)\)
\(15x^3y^2+10x^2y^2-2x^2y^3\)
\(=x^2y^2\left(15x+10-2y\right)\)
`15x^3 y^2 + 10x^2 y^2 - 2x^2 y^3`
`=x^2y^2(15x+10-2y)`