Phân tích đa thức thành nhân tử:
\(6xy+5x-5y-3x^2-3y^2\)
\(=-3x^2+6xy-3y^2+5x-5y\)
\(=-3\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)
\(=-3\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left[-3\left(x-y\right)+5\right]\)
\(=\left(x-y\right)\left(-3x+3y+5\right)\)
Thực hiện phép tính:
a)\(\left(x^2+x-3\right)\left(x^2-x+3\right)\)
\(=\left[x^2+\left(x-3\right)\right]\left[x^2-\left(x-3\right)\right]\)
\(=\left(x^2\right)^2-\left(x-3\right)^2\)
\(=x^4-\left(x^2-6x+9\right)\)
\(=x^4-x^2+6x-9\)
b)\(\left(5x-1\right)\left(x+3\right)-\left(x-2\right)\left(5x-4\right)\)
\(=\left(5x^2+15x-x-3\right)-\left(5x^2-4x-10x+8\right)\)
\(=5x^2+15x-x-3-5x^2+4x+10x-8\)
\(=28x-11\)
Tính nhanh:
a)\\(2004^2-16\\)
\\(=2004^2-4^2\\)
\\(=\\left(2004-4\\right)\\left(2004+4\\right)\\)
\\(=2000.2008\\)
\\(=40160000\\)
b)\\(892^2+892.216+108^2\\)
\\(=892^2+2.892.108+108^2\\)
\\(=\\left(892+108\\right)^2\\)
\\(=1000^2\\)
\\(=1000000\\)
c)\\(10,2.9,8-9,8.0,2+10,2^2-10,2.0,2\\)
\\(=9,8\\left(10,2-0,2\\right)+10,2\\left(10,2-0,2\\right)\\)
\\(=9,8.10+10,2.10\\)
\\(=10\\left(9,8+10,2\\right)\\)
\\(=10.20\\)
\\(=200\\)
