Video Transcript
By identifying the GCF of the
terms, factorize the expression seven 𝑛 times seven 𝑥 minus eight 𝑦 plus six 𝑚
times eight 𝑦 minus seven 𝑥.
In this question, we are asked to
factor an expression by first identifying the GCF of the terms, that is, the
greatest common factor. To do this, we need to check for
common factors among the two terms of the expression.
We can start by checking the
coefficients. The coefficients of the two terms
are seven and six. The greatest common factor of these
integers is one, so we cannot take out a factor from these coefficients. In a similar way, we can see that
the first term has a factor of 𝑛. However, the second term has no
factor of 𝑛.
We can then note that the first
term has a factor of seven 𝑥 minus eight 𝑦. This is very similar to a factor in
the second term, with the only difference being the signs of the terms in the factor
are switched.
If we take a factor of negative one
out of the second term, then we can rewrite the expression as seven 𝑛 times seven
𝑥 minus eight 𝑦 minus six 𝑚 times seven 𝑥 minus eight 𝑦. We can then see that each of the
two terms share a factor of seven 𝑥 minus eight 𝑦. So we can factor this out of the
expression. This gives us seven 𝑛 minus six 𝑚
multiplied by seven 𝑥 minus eight 𝑦.
We can then note that each factor
is linear. And we cannot take out any common
factor from these linear factors. So we cannot factor any
further.
Hence, our answer is seven 𝑛 minus
six 𝑚 multiplied by seven 𝑥 minus eight 𝑦.
