Answer
$$5a$$
Work Step by Step
We're given the expression
$$2(a-3b) + 3(2b+a)$$
By the distributive property of scalar multiplication over vector addition (Theorem 1.1.e), we get:
$$2a+2(-3)b + 3(2b)+3a$$
By the associative property of scalar-vector multiplication (Theorem 1.1.g), we get:
$$2a-6b + 6b+3a$$
Using the commutativity (Theorem 1.1.a) and associativity (Theorem 1.1.b) of vector addition, we rearrange to get:
$$(2a+3a) + (-6b + 6b)$$
By applying the distributive property of vector-scalar multiplication over scalar addition (Theorem 1.1.f), we get:
$$(2+3)a + (-6+6)b$$
With scalar addition, we condense to:
$$5a + 0b$$
And by the identity property of vector addition (Theorem 1.1.c), we get
$$5a$$
