If u = (4, -3) and v = (-2, 7), what is u + v?

Add vectors component by component: $(4+(-2),\ -3+7)=(2,4)$, choice D. The first components are $4$ and $-2$, which sum to $2$, and the second components are $-3$ and $7$, which sum to $4$. Choice B, $(6,-10)$, subtracts the second vector from the first, $(4-(-2),\ -3-7)$. Choice C, $(-8,-21)$, multiplies the components, which is not the operation requested. Choice A, $(2,-4)$, adds the first components correctly but loses the sign of the $7$ in the second. Vector addition is done separately on the $x$-components and $y$-components, taking care with negative signs.