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4. Regroup the terms and factorise: z – 19 + 19xy – xyz

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As an experienced tutor registered on UrbanPro.com, I understand the importance of providing clear and concise explanations to help students grasp challenging concepts. In this response, I will break down the expression "z – 19 + 19xy – xyz" step by step, ensuring a thorough understanding...
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As an experienced tutor registered on UrbanPro.com, I understand the importance of providing clear and concise explanations to help students grasp challenging concepts. In this response, I will break down the expression "z – 19 + 19xy – xyz" step by step, ensuring a thorough understanding for Class 7 students seeking online coaching.

Step 1: Identify Common Factors

  • Factorizing the expression involves identifying common factors among the terms.

  • Observe that "z" is a common factor in the terms "z" and "-xyz."

    Factorized expression: z(1 - y) - 19 + 19xy

Step 2: Simplify Further

Now, let's simplify the remaining terms.

  1. Combine Like Terms:

    • Combine the constant terms "-19" and the simplified expression "z(1 - y) - 19 + 19xy."

      Simplified expression: z(1 - y) + 19xy - 38

  2. Factorize the Constant Terms:

    • Observe that "19" and "38" have a common factor of 19.

      Simplified and factorized expression: z(1 - y) + 19(x - 2y)

Conclusion:

In conclusion, the expression "z – 19 + 19xy – xyz" can be factorized as follows:

z(1−y)+19(x−2y)z(1−y)+19(x−2y)

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