### Video Transcript

Factorize fully nine 𝑥𝑚 minus
four 𝑙𝑧 plus four 𝑙𝑥 minus nine 𝑚𝑧.

In the expression given, there is
no common factor among all four terms apart from one. And we will therefore factorize the
expression by grouping pairs of terms. If we consider the first and last
terms, we note that they have a common factor of nine 𝑚. So we can factor this out. Nine 𝑥𝑚 minus nine 𝑚𝑧 can be
rewritten as nine 𝑚 multiplied by 𝑥 minus 𝑧. We can use the same method when
grouping the second and third terms. These have a common factor of four
𝑙. Negative four 𝑙𝑧 plus four 𝑙𝑥
can be rewritten as four 𝑙 multiplied by negative 𝑧 plus 𝑥. Altering the order of the terms in
the parentheses, we have four 𝑙 multiplied by 𝑥 minus 𝑧.

We now have an equivalent form to
the original expression. At this stage, our two terms have a
common factor of 𝑥 minus 𝑧. Factoring this out, we have 𝑥
minus 𝑧 multiplied by nine 𝑚 plus four 𝑙. This is the fully factored form of
nine 𝑥𝑚 minus four 𝑙𝑧 plus four 𝑙𝑥 minus nine 𝑚𝑧.

Whilst it is not required in this
question, we could check our answer by distributing the parentheses using the FOIL
method. Multiplying the first terms gives
us nine 𝑥𝑚. Multiplying the outer terms gives
us four 𝑙𝑥. The inner terms have a product of
negative nine 𝑚𝑧. And the last terms multiply to give
us negative four 𝑙𝑧. This is the same expression as in
the question.