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\(\left(xy+1\right)^2-\left(x-y\right)^2=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
\(=x^2y^2+xy-x^2y+xy^2+xy+1-x+y+x^2y+x-x^2+xy-xy^2-y+xy-y^2\)
\(=x^2y^2+2xy-x^2-y^2+1\)
Nhân ra thôi mà Huy, mà đánh cái đề cũng nhầm hả?? :D
(x3 + x2y + xy2 +y3)(x - y) = x4 + x3y + x2y2 + xy3 - x3y - x2y2 - xy3 - y4 = x4 - y4 ĐPCM
a) \(25x^2-y^2+4y-4\)
\(=\left(5x\right)^2-\left(y-2\right)^2\)
\(=\left(5x-y+2\right)\left(5x+y-2\right)\)
b) \(x+2y-xy-2\)
\(=\left(x-xy\right)+\left(2y-2\right)\)
\(=x\left(1-y\right)+2\left(y-1\right)\)
\(=x\left(1-y\right)-2\left(1-y\right)\)
\(=\left(1-y\right)\left(x-2\right)\)
\(\left(x+1\right)^2-3\left(x+1\right)=\left(x+1\right)\left(x+1-3\right)=\left(x+1\right)\left(x-2\right)\)
\(2x\left(x-2\right)-\left(x-2\right)^2=\left(x-2\right)\left[2x-\left(x-2\right)\right]=\left(x-2\right)\left(2x-x+2\right)=\left(x-2\right)\left(x+2\right)\)
\(4x^2-20xy+25y^2=\left(2x\right)^2-2.2x.5y+\left(5y\right)^2=\left(2x-5y\right)^2\)
\(x^2+3x-x-3=x\left(x+3\right)-\left(x+3\right)=\left(x-1\right)\left(x+3\right)\)
\(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right)\)
\(2y\left(x+2\right)-3x-6=2y\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(2y-3\right)\)
\(\left(x^2+xy\right)^2-\left(y^2+xy\right)^2=\left(x^2+xy+y^2+xy\right)\left(x^2+xy-y^2-xy\right)\)
\(=\left(x+y\right)^2\left(x-y\right)^2\)
LÀM TIẾP NHA
\(=\left(x^2-xy+xy+y^2\right)^2=\left(x^2+y^2\right)^2=x^4+2x^2y^2+y^4\)