\(1,x^2+2xy+x+2y\)
\(=\left(x^2+2xy\right)+\left(x+2y\right)\)
\(=x\left(x+2y\right)+\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x+1\right)\)
\(2,x^2-10x+25\)
\(=x^2-2.x.5+5^2\)
\(=\left(x-5\right)^2\)
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\(3,x^3+3x^2+3x+1\)
\(=\left(x^3+1\right)+\left(3x^2+3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+3x\right)\)
\(=\left(x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x+1\right)\left(x+1\right)^2\)
\(=\left(x+1\right)^3\)
\(4,x^3-8\)
\(=x^3-2^3\)
\(=\left(x-2\right)\left(x^2+2x+4\right)\)
\(5,x^3+27\)
\(=x^3+3^3\)
\(=\left(x+3\right)\left(x^2-3x+9\right)\)
\(6,x^3-\dfrac{1}{8}\)
\(=x^3-\left(\dfrac{1}{2}\right)^3\)
\(=\left(x-\dfrac{1}{2}\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)
\(7,x^3-x+y^3-y\)
\(=\left(x^3+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
\(8,4x^2-1\)
\(=\left(2x\right)^2-1^2\)
\(=\left(2x-1\right)\left(2x+1\right)\)
\(9,49x^2-9\)
\(=\left(7x\right)^2-3^2\)
\(=\left(7x-3\right)\left(7x+3\right)\)