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Question
Factorise the following:
20(x – y)2 – 30(x – y)3
Sum
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Solution
Given expression: 20(x – y)2 – 30(x – y)3
Step 1: Extract common factors stepwise.
Notice that 20 and 30 have a common factor 10 and both terms include (x – y)2 as a factor:
20(x – y)2 – 30(x – y)3 = 10(x – y)2 × [2 – 3(x – y)]
Step 2: Expand inside the bracket:
2 – 3(x – y) = 2 – 3x + 3y
Thus, 20(x – y)2 – 30(x – y)3 = 10(x – y)2(2 – 3x + 3y).
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