=(x+7)^2-(3x)^2

=(x+7-3x)(x+7+3x)

=(7-2x)(7+4x)

\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)

a)\(3x^2-5x-2=3x^2-6x+x-2=3x\left(x-2\right)+\left(x-2\right)\)

\(=\left(3x+1\right)\left(x-2\right)\)

\(x^3-9x^2+14x=x\left(x^2-9x+14\right)\)

\(=x\left(x^2-2x-7x+14\right)=x\left(x\left(x-2\right)-7\left(x-2\right)\right)\)

\(=x\left(x-7\right)\left(x-2\right)\)

1.2x^2+x-6=2x^2+4x-3x+6=(2x^2+4x)-(3x+6)=2x(x+2)-3(x+2)=(x+2)(2x-3)

2.x^3-9x^2+14x

=x*(x^2-9x+14)

=x*(x^2-7x-2x+14)

=x*((x^2-7x)-(2x-14))

=x*(x(x-7)-2(x-7))

=x*((x--7)(x-2))

=x*(x-7)(x-2)

1) 

\(=\left(x-7\right)^2-4a^2\)

\(=\left(x-7+2a\right)\left(x-7-2a\right)\)

2)

\(=\left(3x+1\right)^2-5^2\)

\(=\left(3x+1+5\right)\left(3x+1-5\right)\)

\(=\left(3x+6\right)\left(3x-4\right)\)

\(=3\left(x+2\right)\left(3x-4\right)\)

1)x^2-14x+49-4a^2

=x^2-2x7+7^2-4a^2

=\(\left(x-7\right)^2-4a^2\)

=\(\left(x-7\right)^2-\left(2a\right)^2\)

=\(\left(\left(x-7\right)-\left(2a\right)\right).\left(\left(x-7\right)+\left(2a\right)\right)\)

=\(\left(x-7-2a\right).\left(x-7+2a\right)\)

b)

\(9x^2+6x+1-25\\ =\left(3x\right)^2-5^2+6x+1\\ =\left(\left(3x\right)-5\right).\left(\left(3x\right)+5\right)+6x+1\)

\(=\left(3x-5\right).\left(3x+5\right)+6x+1\)