[tex]\displaystyle\\
a) (x+2)^2= (x+2)(x+2) \\\\
b)(2x-1)^2-x^2=(2x-1-x)(2x-1+x)=(x-1)(3x-1) \\\\
c) (3x+2)^2-25x^2= (3x+2-5x)(3x+2+5x)=(2x+2)(8x+2)\\\\
d)(8x-3)^2-(2x+5)^2=(8x-3-(2x+5))(8x-3+(2x+5))=\\
=(8x-3-2x-5)(8x-3+2x+5)=(6x-8)(10x+2)\\\\
e)(4x+1)^2-(x^2-4x)^2=(4x+1-(x^2-4x))(4x+1+(x^2-4x))= \\
=(4x+1-x^2+4x)(4x+1+x^2-4x)=(-x^2+8x+1)(x^2+1) \\\\
f)4x^2-(x^2-5x)^2 =(2x-(x^2-5x))(2x+(x^2-5x))=\\
=(2x-x^2+5x)(2x+x^2-5x)=(7x-x^2)(-3x+x^2)=\\
=x(7-x) \times x(x-3)=x^2(7-x)(x-3)[/tex]
