Question Video: Factorizing by Grouping | Nagwa Question Video: Factorizing by Grouping | Nagwa

Question Video: Factorizing by Grouping Mathematics • Second Year of Preparatory School

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Factorize fully 9𝑥𝑚 − 4𝑙𝑧 + 4𝑙𝑥 − 9𝑚𝑧.

02:22

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.

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