a) -7x² + 5xy +12y²

=-7x²-7xy+12xy+12y²

=-7x(x+y)+12y(x+y)

=(x+y)(12y-7x)

b) x⁸ + 3x⁴ + 4

=x⁸+4x⁴+4-x⁴

=(x⁴+2)²-x⁴

=(x⁴-x²+2)(x⁴+x²+2)

=(x⁴+x²-2x²+2)(x⁴+x²+2)

=[x²(x+1)-2(x+1)](x⁴+x²+1)

=(x+1)(x²-2)(x⁴+x²+1)

\(x^8+3x^4+4\)

\(=x^8+4x^4+4-x^4\)

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

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

\(x^8+3x^4+4\)

\(=x^8+4x^4+4-x^4\)

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

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

13: =x(a^3-1)-b(a-1)

=x(a-1)(a^2+a+1)-b(a-1)

=(a-1)(a^2x+a*x+x-b)

12: =(x-y)(x+y)-(x-y)

=(x-y)(x+y-1)

10: =3(x^2-4y^2)

=3(x-2y)*(x+2y)

7: =x^2-x-5x+5=(x-1)(x-5)

8: =x^2+3x+4x+12=(x+3)(x+4)

9: =2x^2-6x-x+3=(x-3)(2x-1)

\(y^2-12y+36-144x^2=\left(y-6\right)^2-\left(12x\right)^2=\left(y-12x-6\right)\left(y+12x-6\right)\)

\(=\left(y^2-12y+36\right)-144x^2=\left(y-6\right)^2-144x^2=\left(y-12x-6\right)\left(y+12x-6\right)\)

\(( y − 12 x − 6 ) ( y + 12 x − 6 )\)

\(12y-9x^2+36-3x^2y\)

\(=\left(36-9x^2\right)-\left(3x^2y-12y\right)\)

\(=-9\left(x^2-4\right)-3y\left(x^2-4\right)\)

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

\(12y-9x^2+36-3x^2y\)

\(=\left(12y-3x^2y\right)-\left(9x^2-36\right)\)

\(=3y\left(4-x^2\right)-9\left(x^2-4\right)\)

\(=3y\left(4-x^2\right)+9\left(4-x^2\right)\)

\(=\left(3y+9\right)\left(4-x^2\right)\)

\(=3\left(y+3\right)\left[\left(2^2\right)-x^2\right]\)

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

=(−3)(x−2)(x+2)(3+y)

5 x² - 5xy+2x−2y = 2x ( x - y) + 2( x - y) = 2( x + 1)( x - y)

\(=\left(12x^2-18xy+9x\right)+\left(8xy-12y^2+6y\right)-\left(4x-6y+3\right)\)

\(=3x\left(4x-6y+3\right)+2y\left(4x-6y+3\right)-\left(4x-6y+3\right)\)

\(=\left(4x-6y+3\right)\left(3x+2y-1\right)\)