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2 (a) Simplify - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

Question 2

2 (a) Simplify. (i) $a^6 + a^2$ (ii) $(b^5)^3$ (b) Factorise. $6x - x^2$

Worked Solution & Example Answer:2 (a) Simplify - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

Step 1

(i) $a^6 + a^2$

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Answer

To simplify the expression $a^6 + a^2$ , we can factor out the common factor. The greatest common factor between the two terms is $a^2$ . Therefore, we have:

$a^6 + a^2 = a^2(a^4 + 1)$

Step 2

(ii) $(b^5)^3$

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Answer

To simplify the expression $(b^5)^3$ , we will apply the power of a power property of exponents, which states that $(x^m)^n = x^{mn}$ . Thus, we get:

$(b^5)^3 = b^{5 imes 3} = b^{15}$

Step 3

(b) Factorise. $6x - x^2$

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Answer

To factorise the expression $6x - x^2$ , we begin by noticing that both terms have a common factor, which is $x$ . Therefore, we can factor $x$ out:

$6x - x^2 = x(6 - x)$

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