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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 start by identifying a common factor. The smallest exponent present in the terms is $2$ , so we can factor out $a^2$ :

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

This expression is now simplified.

Step 2

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

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Answer

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

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

Thus, the simplified form is $b^{15}$ .

Step 3

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

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Answer

To factorise the expression $6x - x^2$ , we will first factor out the common term from both parts of the expression. The common factor is $x$ :

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

Thus, the factorised form is $x(6 - x)$ .

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