Question Video: Factorising by Grouping Mathematics

Completely factor: 4๐‘งยฒ๐‘ฅ โˆ’ ๐‘ง๐‘ฅยฒ + 4๐‘›๐‘ง โˆ’ ๐‘›๐‘ฅ.


Video Transcript

Completely factor four ๐‘ง squared ๐‘ฅ minus ๐‘ง๐‘ฅ squared plus four ๐‘›๐‘ง minus ๐‘›๐‘ฅ.

Here, we can factor by grouping. And we do so by grouping the first two terms together and the last two terms together. And now, we take out a greatest common factor from each set of parentheses. We can take out a ๐‘ง and an ๐‘ฅ from the first set. And if we would take out ๐‘ง and ๐‘ฅ from both of these terms, we would be left with four ๐‘ง minus ๐‘ฅ.

And out of the last two terms, we can take out an ๐‘›. So the ๐‘› is our GCF โ€” our greatest common factor. And once we take that out, we are left with four ๐‘ง minus ๐‘ฅ. So the greatest common factors come together to be one factor. And then these matching terms become another factor.

So our final answer is ๐‘ง๐‘ฅ plus ๐‘› times four ๐‘ง minus ๐‘ฅ.

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