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1 (a) Simplify $(xy)^y$ - Edexcel - GCSE Maths - Question 2 - 2022 - Paper 2

Question 2

1 (a) Simplify $(xy)^y$. (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 $(xy)^y$ - Edexcel - GCSE Maths - Question 2 - 2022 - Paper 2

Step 1

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Answer

To simplify $(xy)^y$ , we can apply the property of exponents that states $(ab)^n = a^n b^n$ . Thus:

$(xy)^y = x^y y^y$

The simplified expression is therefore $x^y y^y$ .

Step 2

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Answer

First, expand both expressions:

$4(x + 3) = 4x + 12$

$7(4 - 2x) = 28 - 14x$

Now, combine the results:

$4x + 12 + 28 - 14x$

Combine like terms:

$(4x - 14x) + (12 + 28) = -10x + 40$

The simplified expression is $-10x + 40$ .

Step 3

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Answer

To factorise the expression $15x^2 + 3xy$ , first identify the common factor:

The greatest common factor is $3x$ , so we can factor it out:

$15x^2 + 3xy = 3x(5x + y)$

The fully factorised form is $3x(5x + y)$ .

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