factories
(v) z - 7+ 7 x y - xyz
Answers
Step-by-step explanation:
z - 7 + 7xy - xyz
= (z - 7) + xy(7 - z)
= (z - 7) - xy(z - 7)
= (z - 7)(1 - xy)
Answer :
›»› The factorization of z - 7 + 7xy - xyz is -(z - 7) (xy - 1).
Given :
- z - 7 + 7xy - xyz.
To Solve :
- Factorize the expression.
Solution :
→ z - 7 + 7xy - xyz
→ -xyz + 7xy + z - 7
→ -(xyz - 7xy - z + 7)
→ -((z - 7) (xy - 1))
→ -(z - 7) (xy - 1)
Explanation :
Let's start our explanation and understand the steps to get our final result of factorization.
→ z - 7 + 7xy - xyz
Regroup terms,
→ -7 + z + 7xy - xyz
Move z,
→ -7 + 7xy - xyz + z
Reorder 7xy and -xyz,
→ -7 - xyz + 7xy + z
Factor -1 out of -xyz,
→ -7 - (xyz) + 7xy+ z
Factor -1 out of 7xy,
→ -7 - (xyz) - (-7xy) + z
Factor -1 out of z,
→ -7 - (xyz) - (-7xy) - 1(-z)
Factor -1 out of -(xyz) - (-7xy),
→ -7 - (xyz 7xy) - 1 (-z)
Factor -1 out of -(xyz - 7xy) -1(-2),
→ -7 - (xyz - 7zy - z)
Reorder -7 and - (xyz - 7xy - z),
→ -(xyz - 7xy - z) – 7
Rewrite -7 as -1(7),
→ -(xyz - 7xy - z) - 1(7)
Factor -1 out of -(xyz - 7xy - z) -1(7),
→ -(xyz - 7xy - z + 7)
Group the first two terms and the last two terms,
→ -((xyz - 7xy) -z + 7)
Factor out the greatest common factor (GCF) from each group,
→ -(xy (z - 7) - (z - 7))
Factor the polynomial by factoring out the greatest common factor, z - 7,
→ -((z - 7) (xy - 1))
Remove unnecessary parentheses,
→ -(z - 7) (xy - 1)
Hence, the factorization of z - 7 + 7xy - xyz is -(z - 7) (xy - 1).
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