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10 (a) Simplify: 3c^2 d \times 2d (b) Factorise - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

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10-(a)-Simplify:-3c^2-d-\times-2d--(b)-Factorise-OCR-GCSE Maths-Question 10-2021-Paper 1.png

10 (a) Simplify: 3c^2 d \times 2d (b) Factorise. 35x + 7x^2

Worked Solution & Example Answer:10 (a) Simplify: 3c^2 d \times 2d (b) Factorise - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

Step 1

Simplify: 3c^2 d \times 2d

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Answer

To simplify the expression, we multiply the coefficients and combine like terms:

  1. Multiply the coefficients:

    3×2=63 \times 2 = 6

  2. Combine the variables according to the laws of exponents:

    d×d=d2d \times d = d^2

    Thus, the complete simplified expression is:

    6c2d26c^2 d^2

Step 2

Factorise. 35x + 7x^2

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Answer

To factorise the expression, we look for the greatest common factor (GCF).

  1. The GCF of the coefficients 35 and 7 is 7.

  2. Both terms have an 'x' as a common factor.

So we can factor out 7x:

7x(5+x)7x(5 + x)

Thus, the fully factorised form is:

7x(5+x)7x(5 + x)

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