Tonight’s tidbit hails from a week filled with finals or finals preparation for nearly all of my students. One of the skills I found myself reminding many of them of is the distributive property.
The distributive property says that you multiply each term of a polynomial by the same monomial and get the same answer you would have if you’d solved the polynomial first and then multiplied the result by the monomial.
That was pretty technical. Let’s look at it symbolically:
a(b + c) = ab + ac
Just to help it make even more sense, let’s throw in some numbers to see what happens on both sides of the equal sign:
3(2 +5) = 3*2 + 3*5
3(7) = 6 +15
21 = 21
Check it out! Both sides simplified to 21! Pretty neat, right? But I can already hear you asking where you would really use this, since it’s obvious from order of operations that we would just add the 2 and 5 before multiplying by the 3.
But what if we didn’t know the value of what was inside the parentheses?
12(x + 3) =96
We can’t just simplify the left side thanks to that variable. We can, however, distribute the 12 and then solve for x.
12x + 12*3 = 96 (Distribute the 12.)
12x + 36 = 96 (Multiply the 12 and 3.)
12x = 60 (Subtract 36 from both sides of the equation.)
x = 5 (Divide both sides by 12.)
When we distribute, it’s important to remember to distribute across all of the terms in the polynomial.
Correct: 12(x2 + x + 2) = 12x2 + 12x + 24 Incorrect: 3(2x +5) = 6x + 5
And Dead Bunny reminds us all to double check our work for minor errors. Distributing is one of most common places to make silly math mistakes.
