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

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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:

  1. Expand each term:

    • For the first term: 5(x−2)=5x−105(x-2) = 5x - 10
    • For the second term: −2(x−4)=−2x+8-2(x-4) = -2x + 8

  2. Combine the results: 5x−10−2x+85x - 10 - 2x + 8 = 3x−23x - 2

Thus, the final answer is:

3x−23x - 2

Step 2

Factorise fully; 10x² + 6x

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Answer

To factorise the quadratic expression:

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

The fully factorised form is:

2x(5x+3)2x(5x + 3)

Step 3

Simplify. (x⁵)²

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Answer

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

  1. Use the formula: (am)n=amimesn(a^m)^n = a^{m imes n} Thus, (x5)2=x5imes2=x10(x^5)^2 = x^{5 imes 2} = x^{10}

The simplified form is:

x10x^{10}

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