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Question
Factorise the following:
8 – 2(x – 1)2
Sum
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Solution
Given: 8 – 2(x – 1)2
Step-wise calculation:
1. Write the expression as:
8 – 2(x – 1)2 = 2 × 4 – 2(x – 1)2
8 – 2(x – 1)2 = 2[4 – (x – 1)2]
2. Recognize the difference of squares inside the bracket:
4 – (x – 1)2 = (2)2 – (x – 1)2
4 – (x – 1)2 = (2 – (x – 1))(2 + (x – 1))
3. Simplify each factor:
2 – (x – 1) = 2 – x + 1
2 – (x – 1) = 3 – x
2 + (x – 1) = 2 + x – 1
2 + (x – 1) = 1 + x
4. Substitute back:
2[(3 – x)(1 + x)]
5. Optionally, rewrite as:
2(3 – x)(x + 1)
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