Question Video: Factorizing by Taking Out the Greatest Common Factor Mathematics • First Year of Preparatory School

Video Transcript

Factor fully 𝑎 minus 10 times 𝑎 plus eight minus two times 𝑎 plus eight.

Given the expression 𝑎 minus 10 times 𝑎 plus eight minus two times 𝑎 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 𝑎 minus 10 and a factor of 𝑎 plus eight. And the second term has the factors negative two and 𝑎 plus eight, which means both terms share a factor of 𝑎 plus eight. And that means we can undistribute the factor of 𝑎 plus eight. In our first term, if we take out the factor 𝑎 plus eight, the factor remaining will be 𝑎 minus 10.

In our second term, if we remove 𝑎 plus eight, we’ll be left with negative two. We’ve now rewritten our original expression as 𝑎 plus eight times 𝑎 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 𝑎 plus eight times 𝑎 minus 10 minus two. And 𝑎 minus 10 minus two equals 𝑎 minus 12. A fully factorized form of the original expression would look like this. 𝑎 plus eight times 𝑎 minus 12.