1 (a) Simplify $(x^y)^{y}$
(b) Expand and simplify $4(x + 3) + 7(4 - 2x)$
(c) Factorise fully $15x^2 + 3xy$
(Total for Question 1 is 5 marks)
Worked Solution & Example Answer:1 (a) Simplify $(x^y)^{y}$
(b) Expand and simplify $4(x + 3) + 7(4 - 2x)$
(c) Factorise fully $15x^2 + 3xy$
(Total for Question 1 is 5 marks) - Edexcel - GCSE Maths - Question 1 - 2022 - Paper 2
Step 1
Simplify $(x^y)^{y}$
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Answer
To simplify (xy)y, we use the power of a power rule which states that (am)n=am⋅n. Therefore:
(xy)y=xy⋅y=xy2
Thus, the final simplification is:
xy2
Step 2
Expand and simplify $4(x + 3) + 7(4 - 2x)$
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Answer
Distribute the terms:
For the first part: 4(x+3)=4x+12
For the second part: 7(4−2x)=28−14x
Combine like terms:
Combine the results from above: 4x+12+28−14x=(4x−14x)+(12+28)=−10x+40
Thus, the final expanded and simplified expression is:
−10x+40
Step 3
Factorise fully $15x^2 + 3xy$
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Answer
To factorise the expression 15x2+3xy, we first look for the greatest common factor (GCF). In this case, the GCF of 15x2 and 3xy is 3x. We can factor this out:
