(2-3y)(9y^2+6y+4)=(2-3y)(3y+2)^2
(x+2)^3-(x-2)^3
=(x+2-x+2)[(x+2)^2+(x+2)(x-2)+(x-2)^2]
=4(3x^2+4)
1/2*x^4-8
=1/2*(x^4-16)
=1/2*(x^2-4)(x^2+4)
=1/2*(x-2)(x+2)(x^2+4)
x^4+7x^2-8
=(x^2-1)(x^2+8)
=(x-1)(x+1)(x^2+8)
a^4-a^3+a^2-a
=a^3(a-1)+a(a-1)
=a(a-1)(a^2+1)
4a^2-9b^2+c^2-4ac
=4a^2-4ac+c^2-(3b)^2
=(2a-c)^2-(3b)^2
=(2a-c+3b)(2a-c-3b)
(ax+by)^2+(bx-ay)^2
=(ax)^2+2abxy+(by)^2+(bx)^2-2abxy+(ay)^2
=(ax)^2+(by)^2+(bx)^2+(ay)^2
=a^2(x^2+y^2)+b^2(x^2+y^2)
=(a^2+b^2)(x^2+y^2)