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x^7+x^5+1=x^7+x^6+x^5-x^6+1
=x^5(x^2+x+1)-[(x^3)^2-1]
=x^5(x^2+x+1)-(x^3+1)(x^3-1)
=x^5(x^2+x+1)-(x^3+1)(x-1)(x^2+x+1)
=(x^2+x+1)[x^5-(x^3+1)(x-1)]
=(x^2+x+1)(x^5-x^4+x^3-x+1)
a, \(\left(3x-6y\right)x+y\left(x-2y\right)=\left(3x+y\right)\left(x-2y\right)\)
b, \(3\left(x-y\right)-5x\left(y-x\right)=\left(3+5x\right)\left(x-y\right)\)
c, \(\dfrac{2}{5}x\left(y-1\right)+\dfrac{2}{5}y\left(1-y\right)=\left(\dfrac{2}{5}x-\dfrac{2}{5}y\right)\left(y-1\right)=\dfrac{2}{5}\left(x-y\right)\left(y-1\right)\)
d, \(x\left(x-1\right)-y\left(1-x\right)=\left(x+y\right)\left(x-1\right)\)
a)x2-xy+x-y
=x(x-y)+(x-y)
=(x+1)(x-y)
b)3x2-3xy-5x+5y
=3x(x-y)-5(x-y)
=(3x-5)(x-y)
a ) \(x^2-xy+x-y\).
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right).\)
b ) \(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
\(y\cdot\left(x-y\right)-5x+5y=y\cdot\left(x-y\right)-5\cdot\left(x-y\right)=\left(x-y\right)\cdot\left(y-5\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x+y-5\right)\left(x-y\right)\)
a: \(=3\left[\left(m-5\right)^3+8\right]\)
\(=3\left(m-5+2\right)\left[\left(m-5\right)^2-2\left(m-5\right)+4\right]\)
\(=3\left(m-3\right)\left(m^2-10m+25-2m+10+4\right)\)
\(=3\left(m-3\right)\left(m^2-12m+39\right)\)
b: \(=5\left(1-6k\right)^3-5\cdot64\)
\(=5\left(1-6k-4\right)\left[\left(1-6k\right)^2+4\left(1-6k\right)+16\right]\)
\(=5\left(-6k-3\right)\left(36k^2-12k+1+4-24k+16\right)\)
\(=-15\left(2k+1\right)\left(36k^2-36k+21\right)\)
\(=-45\left(2k+1\right)\left(12k^2-12k+7\right)\)
c: \(=\left(a+b-2b+a\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(2b-a\right)+\left(2b-a\right)^2\right]\)
\(=\left(2a-b\right)\left(a^2+2ab+b^2+2ab-a^2+2b^2-ab+4b^2-4ab+b^2\right)\)
\(=\left(2a-b\right)\cdot b\cdot\left(6b+a\right)\)
\(3x\left(x-y\right)+5y\left(y-x\right)\)
\(=3x\left(x-y\right)-5y\left(x-y\right)\)
\(=\left(3x-5y\right)\left(x-y\right)\)