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10 (a) Simplify \[ \frac{x - 1}{5(x - 1)^2} \] (b) Factorise fully \[50 - 2y^2\] - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 1
Question 11
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10 (a) Simplify \[ \frac{x - 1}{5(x - 1)^2} \] (b) Factorise fully \[50 - 2y^2\]
Worked Solution & Example Answer:10 (a) Simplify \[ \frac{x - 1}{5(x - 1)^2} \] (b) Factorise fully \[50 - 2y^2\] - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 1
Step 1
Simplify \[ \frac{x - 1}{5(x - 1)^2} \]
Answer
To simplify the expression, we can start by factoring out the common term in the numerator and denominator:
[
\frac{x - 1}{5(x - 1)^2} = \frac{1}{5(x - 1)}
]
This leaves us with (\frac{1}{5(x - 1)}), since the ((x - 1)) in the numerator cancels out one of the ((x - 1)) in the denominator.
Step 2
Factorise fully \[50 - 2y^2\]
Answer
In this expression, we notice that we can factor out a common factor of 2:
[50 - 2y^2 = 2(25 - y^2)]
Next, we observe that (25 - y^2) is a difference of squares, which can be factored further:
[25 - y^2 = (5 - y)(5 + y)]
Putting it all together, we get the fully factored form:
[50 - 2y^2 = 2(5 - y)(5 + y)]