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4 a) Simplify: (i) 5x - 6y - x + 3y (ii) w^8 + w^2 (iii) 5c^2d × 3c (b) Work out the value of (i) 4x - 7 when x = 5, (ii) \frac{p + 7}{3} when p = 2. - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

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4--a)-Simplify:--(i)-5x---6y---x-+-3y--(ii)-w^8-+-w^2--(iii)-5c^2d-×-3c--(b)-Work-out-the-value-of--(i)-4x---7-when-x-=-5,--(ii)-\frac{p-+-7}{3}-when-p-=-2.-OCR-GCSE Maths-Question 4-2018-Paper 1.png

4 a) Simplify: (i) 5x - 6y - x + 3y (ii) w^8 + w^2 (iii) 5c^2d × 3c (b) Work out the value of (i) 4x - 7 when x = 5, (ii) \frac{p + 7}{3} when p = 2.

Worked Solution & Example Answer:4 a) Simplify: (i) 5x - 6y - x + 3y (ii) w^8 + w^2 (iii) 5c^2d × 3c (b) Work out the value of (i) 4x - 7 when x = 5, (ii) \frac{p + 7}{3} when p = 2. - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

Step 1

(i) 5x - 6y - x + 3y

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Answer

To simplify the expression, start by combining like terms:

  1. Combine the x terms: 5xx=4x5x - x = 4x
  2. Combine the y terms: 6y+3y=3y-6y + 3y = -3y

Thus, the simplified expression is:

4x3y4x - 3y

Step 2

(ii) w^8 + w^2

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Answer

Since there are no like terms to combine, we present the result as:

w8+w2w^8 + w^2

Step 3

(iii) 5c^2d × 3c

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Answer

To simplify the expression, multiply the coefficients and combine the variables using the properties of exponents:

  1. Coefficients: 5×3=155 × 3 = 15
  2. Variables: c2×c=c2+1=c3c^2 × c = c^{2+1} = c^3

Thus, the simplified expression is:

15c3d15c^3d

Step 4

(i) 4x - 7 when x = 5

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Answer

Substituting x=5x = 5 into the expression:

4(5)7=207=134(5) - 7 = 20 - 7 = 13

Step 5

(ii) p + 7 when p = 2

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Answer

Substituting p=2p = 2 into the expression:

2+73=93=3\frac{2 + 7}{3} = \frac{9}{3} = 3

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