\(a,2x^2-4xy+2y^2-8t^2\)
\(=2\left[\left(x^2-2xy+y^2\right)-4t^2\right]\)
\(=2\left[\left(x-y\right)^2-\left(2t^2\right)\right]-\)
\(=2\left(x-y+2t\right)\left(x-y-2t\right)\)
\(b,x^3+x+3x^2y+2xy^2+y^3+y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2+1\right]\)
\(=\left(x+y\right)\left(x^2+2xy+y^2+1\right)\)
\(c,x^4-7x^2=x^2\left(x^2-7\right)\)
\(=x^2\left(x+\sqrt{7}\right)\left(x-\sqrt{7}\right)\)
Sửa đề:\(d,5x-5y-x^2+2xy-y^2\)
\(=5\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(5-x+y\right)\)
\(e,x^4+4x^3+4x^2-x^2y^2\)
\(=\left(x^4+4x^3+4x^2\right)-x^2y^2\)
\(=\left(x^2+2x\right)^2-\left(xy\right)^2\)
\(=\left(x^2+2x+xy\right)\left(x^2+2x-xy\right)\)
\(g,x^2-y^2-2y-1\)
\(=x^2-\left(y+1\right)^2\)
\(=\left(x+y+1\right)\left(x-y-1\right)\)
a) \(2x^2-4xy+2y^2-8t^2=2\left(x^2-2xy+y^2-4t^2\right)\)
\(=2\left(\left(x-y\right)^2-\left(2t\right)^2\right)=2\left(x-y-2t\right)\left(x-y+2t\right)\)
b) \(x^3+x+3x^2y+3xy^2+y^3+y=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)=\left(x+y\right)^2\left(x+y\right)+\left(x+y\right)\)
\(=\left(x^2+2xy+y^2\right)\left(x+y\right)+\left(x+y\right)=\left(x^2+2xy+y^2+1\right)\left(x+y\right)\)
c) \(x^4-7x^2=\left(x^2\right)^2-\left(\sqrt{7}x\right)^2=\left(x^2-\sqrt{7}x\right)\left(x^2+\sqrt{7}x\right)\)
d) câu này hình như đề sai thì phải
e) \(x^4+4x^3+4x^2-x^2y^2=x^2\left(x^2+4x+4-y^2\right)\)
\(=x^2\left(\left(x+2\right)^2-y^2\right)=x^2\left(x+2-y\right)\left(x+2+y\right)\)
g) \(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2\)
\(=\left(x-y-1\right)\left(x+y+1\right)\)
