Odpowiedź:
Szczegółowe wyjaśnienie:
P=ab
P=(x+2x)(3x^2-x)=3x^3-x^2+6x^3-2x^2=9x^3-3x^2
P=(x^3-x)(x+2)=x^4+2x^3-x^2-2x
P=4x*(2-4x^2)=8x-16x^3
P=(2 -3x)*2x=4x-6x^2
Pole prostokąta liczymy ze wzoru:
P = a · b
[tex]A.\\a = x+2x\\b = 3x^{2}-x\\\\P =ab= (x+2x)(3x^{2}-x)=x\cdot3x^{2}+x\cdot(-x) + 2x\cdot3x^{2}+2x\cdot(-x) =\\\\=3x^{3}-x^{2}+6x^{3}-2x^{2}=\boxed{9x^{3}-3x^{2}}[/tex]
[tex]B.\\a = x^{3}-x\\b = x+2\\\\P=ab = (x^{3}-x)(x+2) =\boxed{ x^{4}+2x^{3}-x^{2}-2x}[/tex]
[tex]C.\\a = 4x\\b = 2-4x^{2}\\\\P = ab = 4x(2-4x^{2}) = \boxed{8x-16x^{3}}[/tex]
[tex]D.\\a = 2-3x\\b = 2x\\\\P = ab = (2-3x)\cdot2x = \boxed{4x-6x^{2}}[/tex]