Term matrix and regression model formula

hey, am not sure about the way the regression model is formulated in the help file this model is proposed 'MPG ~ Acceleration + Weight + Acceleration:Weight + Weight^2' with this Term matrix T = [0 0 0;1 0 0;0 1 0;1 1 0;0 2 0] and this Linear regression model: y ~ 1 + x1*x2 + x2^2 Which I found strange compared to the terms Matrix but then I saw that '*' means also all lower order term and the same for ^ so that would be the same as y= 1+x1+x2+x1+x2 +x2^2

Is this correct?

regards,J