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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) ....... (b) Factorise fully; 10x² + 6x (c) Simplify. (x⁵)²

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

Step 1

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Answer

To expand the expression, we distribute the terms:

Start with the expression: $5(x - 2) - 2(x - 4)$
Distributing $5$ and $-2$ :
- The first part: $5(x - 2) = 5x - 10$
- The second part: $-2(x - 4) = -2x + 8$
Now, combine the results: $5x - 10 - 2x + 8$
Combining like terms:
- $5x - 2x = 3x$
- $-10 + 8 = -2$

Thus, the simplified result is:

$3x - 2$

Step 2

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Answer

To factorise the expression $10x^2 + 6x$ fully, we first look for common factors:

Identify the greatest common factor (GCF) of the terms:
- The GCF of $10x^2$ and $6x$ is $2x$ .
Factor out $2x$ : $10x^2 + 6x = 2x(5x + 3)$

Thus, the expression fully factorised is:

$2x(5x + 3)$

Step 3

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Answer

To simplify the expression $(x^5)^2$ , we use the power of a power rule, which states:

$(a^m)^n = a^{m imes n}$

In this case:

Therefore, the simplified result is:

$x^{10}$

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