Distributing Multiplication over Addition and Subtraction
Distributing multiplication over addition (and subtraction) and factoring (the opposite of distributing) are extremely important in algebra. The distributive law of multiplication over addition, a(b + c) = ab + ac, says that you can first take the sum (b + c) then the product (a times the sum of b and c) or the individual products (ab and ac) then the sum (the sum of ab and ac). For instance, 12(6 + 4) could be computed as 12(6 + 4) = 12(6) + 12(4) = 72 + 48 = 120 or as 12(6 + 4) = 12(10) = 120. The distributive law of multiplication over subtraction, a(b – c) = ab – cd, says the same about a product and difference.
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