Expand and simplify. 5(x−2)−2(x−4) (a) .............................................................[2] Factorise fully; 10x² + 6x (b) .............................................................[2] Simplify. (x⁵)² (c) .............................................................[1]

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Expand and simplify - OCR - GCSE Maths - Question 4 - 2017 - Paper 1

Question 4

Expand and simplify. 5(x−2)−2(x−4) (a) .............................................................[2] Factorise fully; 10x² + 6x (b) ............................ show full transcript

Worked Solution & Example Answer:Expand and simplify - OCR - GCSE Maths - Question 4 - 2017 - Paper 1

Step 1

Expand and simplify. 5(x−2)−2(x−4)

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Answer

To expand the expression, distribute the factors:

Expand each term:
- For the first term: $5(x-2) = 5x - 10$
- For the second term: $-2(x-4) = -2x + 8$
Combine the results: $5x - 10 - 2x + 8$ = $3x - 2$

Thus, the final answer is:

$3x - 2$

Step 2

Factorise fully; 10x² + 6x

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Answer

To factorise the quadratic expression:

Factor out the greatest common factor (GCF): $2x(5x + 3)$

The fully factorised form is:

$2x(5x + 3)$

Step 3

Simplify. (x⁵)²

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Answer

To simplify the expression, apply the power of a power rule:

Use the formula: $(a^m)^n = a^{m imes n}$ Thus, $(x^5)^2 = x^{5 imes 2} = x^{10}$

The simplified form is:

$x^{10}$

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