(x-1/2y-1)(x-1/2y +1)-(1/2y-1)^2
=[(x-1/2y)-1][(x-1/2y) +1)]-(1/2y-1)^2
=(x-1/2y)²-1-(1/2y-1)^2
=x²-xy+y²/4-1-(y²/4-y+1)
=x²-xy+y²/4-1-y²/4+y-1
=x²-xy+y-21+ab-a-b 8ax-4ay-6bx+3byx^2-9y^2-4z^2+12yz1/2x^3-4 a^2-2ab+b^2-m^2-2mn-n^21+ab-a-b=(1-a)+(ab-b)=(1-a)+b(a-1)=(1-a)(1-b) 8ax-4ay-6bx+3by=(8ax-4ay)-(6bx-3by)=4a(2x-y)-3b(2x-y)=(2x-y)(4a-3b) x^2-9y^2-4z^2+12yz=x^2-(9y^2+4z^2+12yz)=x^2-(3y+2z)^2=(x+3y+2z)(x-3y-2z)1/2x^3-4 =(1/2)(x^3-8)=(1/2)(x-2)(x^2+2x+4) a^2-2ab+b^2=(a-b)^2 -m^2-2mn-n^2=-(m^2+2mn+n^2)=-(m+n)^2