Video: Factorizing by Taking Out the Greatest Common Factor

Factor fully (π‘Ž βˆ’ 10)(π‘Ž + 8) βˆ’ 2(π‘Ž + 8).

01:33

Video Transcript

Factor fully π‘Ž minus 10 times π‘Ž plus eight minus two times π‘Ž plus eight.

Given the expression π‘Ž minus 10 times π‘Ž plus eight minus two times π‘Ž plus eight, in order to factor this, we need a common factor between the two terms. Here are the two terms. The first term has a factor of π‘Ž minus 10 and a factor of π‘Ž plus eight. And the second term has the factors negative two and π‘Ž plus eight, which means both terms share a factor of π‘Ž plus eight. And that means we can undistribute the factor of π‘Ž plus eight. In our first term, if we take out the factor π‘Ž plus eight, the factor remaining will be π‘Ž minus 10.

In our second term, if we remove π‘Ž plus eight, we’ll be left with negative two. We’ve now rewritten our original expression as π‘Ž plus eight times π‘Ž minus 10 minus two. And within these brackets, we can do some simplification. Since there’s only addition or subtraction inside the brackets, we can remove the parentheses. So, we have π‘Ž plus eight times π‘Ž minus 10 minus two. And π‘Ž minus 10 minus two equals π‘Ž minus 12. A fully factorized form of the original expression would look like this. π‘Ž plus eight times π‘Ž minus 12.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.