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a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5+y\right)\left(x+5-y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(x^2+2\right)\left(5x-7\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5-y\right)\left(x+5+y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(5x-7\right)\left(x^2+2\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
2: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
3: =x^2(x^2+2x+1)
=x^2(x+1)^2
4: =x^2+6x-x-6
=(x+6)(x-1)
5: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
6: =5x(x+y)-(x+y)
=(x+y)(5x-1)
7: =2x^2+5x-2x-5
=(2x+5)(x-1)
8: =(x^2-1)*(x^2-4)
=(x-1)(x+1)(x-2)(x+2)
9: =x^2(x-5)-9(x-5)
=(x-5)(x-3)(x+3)
\(a,=5x^2-5x+3x-3=\left(x-1\right)\left(5x+3\right)\\ b,=2x^2-5x+2x-5=\left(2x-5\right)\left(x+1\right)\\ c,=x^2+5x-3x-15=\left(x+5\right)\left(x-3\right)\\ d,=7x^2-7x+x-1=\left(x-1\right)\left(7x+1\right)\)
C