d) \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left[\left(3x+1\right)-2\left(x-2\right)\right]\left[\left(3x+1\right)+2\left(x-2\right)\right]\)
\(=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)\)
\(=\left(x+5\right)\left(5x-3\right)\)
c) \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left[3\left(2x+3\right)-2\left(x+1\right)\right]\left[3\left(2x+3\right)+2\left(x+1\right)\right]\)
\(=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\)
\(=\left(4x-7\right)\left(8x+11\right)\)
f) \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left[2bc-\left(b^2+c^2-a^2\right)\right]\left[2bc+\left(b^2+c^2-a^2\right)\right]\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
g: =(ax+by-ay-bx)(ax+by+ay+bx)
=[a(x-y)-b(x-y)]*[a(x+y)+b(x+y)]
=(x-y)(x+y)(a-b)(a+b)
h: =(a^2+b^2-5-2ab-4)(a^2+b^2-5+2ab+4)
=[(a-b)^2-9][(a+b)^2-1]
=(a-b-3)(a-b+3)(a+b-1)(a+b+1)
i: =(4x^2-3x-18-4x^2-3x)(4x^2-3x-18+4x^2+3x)
=(-6x-18)(8x^2-18)
=-12(x+3)(4x^2-9)
=-12(x+3)(2x-3)(2x+3)
k: =(3x+3y-3)^2-(4x+6y+2)^2
=(3x+3y-3-4x-6y-2)(3x+3y-3+4x+6y+2)
=(-x-3y-5)(7x+9y-1)
i: =25-(2x-3y)^2
=(5-2x+3y)(5+2x-3y)
m: =(x-y)^2-(2m-n)^2
=(x-y-2m+n)(x-y+2m-n)
