Wzory to:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
b)
[tex]W(x)=x^3+1=(x+1)(x^2-x+1)[/tex]
c)
[tex]W(x)=x^3-8=(x-2)(x^2+2x+4)[/tex]
d)
[tex]W(x)=8x^3-1=(2x-1)(4x^2+2x+1)[/tex]
Korzystamy ze wzorów skróconego mnożenia:
[tex]a^{3}+b^{3} = (a+b)(a^{2}-ab+b^{2})\\a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})[/tex]
[tex]a) \ w(x) = x^{3}+1 = x^{3}+1^{3} = (x+1)(x^{2}-x+1)\\\\b) \ w(x) = x^{3}-8 = x^{3}-2^{3} = (x-2)(x^{2}+2x+4)\\\\c) \ w(x) = 8x^{3}-1 = (2x)^{3}-1^{3} = (2x-1)(4x^{2}+2x+1)[/tex]
