Math CentralQuandaries & Queries


Question from Jordan, a student:

hi i saw a question in class today that i didn't understand and i didn't really understand what my teacher was going on about so how do you factorise 15x + 15y

The simple answer is "not much."
It's linear so the most you can to is extract common scalar ("number") factors: $15(x+y).$ (You could factorize $15$ a $3 \times 5$ but for most purposes that would be pointless.)

Good Hunting!



Suppose you were asked to calculate $9 \times 7 + 9 \times 3.$ You could find $9 \times 7$ and $9 \times 3$ and add the results but you could also notice that you have seven nines and then three more nines so that you have in total ten nines which is ninety. That is $9 \times 7 + 9 \times 3 = 9 \times (7 + 3) = 9 \times 10 = 90.$ This process of extracting a common factor can be applied to your problem also, $15 \times x + 15 \times y = 15 \times (x + y).$


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