Explanation:
A formula can express the distributive property of multiplication over addition:
a(b + c) = ab + ac
When a quantity multiplies a sum in parentheses, the quantity effectively multiplies each of the elements of the sum.
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For example, if you have 5 identical bags that each contain 2 toys and 3 pieces of candy, you have a total of 5×2 = 10 toys and 5×3 = 15 pieces of candy.
5(2t + 3c) = 5(2t) + 5(3c)
= 10t + 15c
This idea is the basis of multi-digit multiplication:
4(12) = 4(10 +2)
= 4·10 + 4·2
= 40 +8
= 48
