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

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

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

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

Step 1

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Answer

To simplify the expression, follow these steps:

Multiply the coefficients:
- The coefficients are 3 and 2.
- Calculate: 3 × 2 = 6.
Multiply the variable parts:
- The variable parts are $c^2$ and $d \times d$ (which is $d^2$ ).
- Thus, combine them: $c^2 \times d^2 = c^2d^2$ .
Combine the results:
- From the calculations, we get: $6c^2d^2$ .

Therefore, the simplified expression is: $6c^2d^2$ .

Step 2

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Answer

To factorise the expression, follow these steps:

Identify the common factor:
- Both terms, $35x$ and $7x^2$ , have a common factor of $7x$ .
Factor out the common factor:
- Divide each term by $7x$ :
- $35x ÷ 7x = 5$
- $7x^2 ÷ 7x = x$
Write the factorised form:
- The expression can be written as: $7x(5 + x)$ .

Thus, the factorised form is: $7x(5 + x)$ .

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