#1: 3t + -6, #2: 0.2y + 0.2(2) = 0.2y + 0.4
Might help to understand why expanding works.
Multiplication is just repeated addition. 4 x 3 is the same as saying 4 + 4 + 4. So when we say 3(t - 2), we're really saying
(t - 2) + (t - 2) + (t - 2).
And if you remove the parentheses and rearrange it, you get
t - 2 + t - 2 + t - 2
t + t + t - 2 - 2 - 2
(t + t + t) + (-2 + -2 + -2)
3t + 3(-2).
Does that make sense? Drawing a picture can help too:
[tex]3 \times (\square + \blacksquare) = \square \blacksquare + \square\blacksquare + \square\blacksquare = (\square\square\square) + (\blacksquare\blacksquare\blacksquare) = (3 \times \square) + (3 \times \blacksquare)[/tex]
Anyway so for #1 we have 3(t - 2), which equals 3(t) + 3(-2), which is 3t + -6.
For #2 we have 0.2(y + 2) = 0.2y + 0.2(2) = 0.2y + 0.4.
