Math CentralQuandaries & Queries


Question from Madison, a student:

3a(7b+6c). The directions are: use the distributive property to rewrite the expression.

Hi Madison,

The distributive property states that for any numbers $x, y$ and $z,$

\[x(y + z) = xy + xz.\]

I want to illustrate its use with a different expression, $5p(6q - 9r).$ Using the distributive property to rewrite this expression I get

\[5p(6q - 9r) = 5p\left(6q + (-9r)\right) = (5p) \times (6q) + (5p) \times (-9r).\]

Since multiplication is commutative, that is for any numbers $x$ and $y, xy = yx,$ my expression above can be rewritten

\[5p(6q - 9r) = 5p\left(6q + (-9r)\right) = (5p) \times (6q) + (5p) \times (-9r) = 30 pq - 45 pr.\]

Now try your expression,

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