Worksheets · Foundation and Higher

Single brackets and common factors

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
Answer each part.
(a) Expand $5(x + 4)$ (1)
(b) Expand and simplify $3(2y - 1) + 4y$ (2)
(c) Factorise $6a + 15$ (1)
Question 2Non-calculator · 4 marks
A pupil is simplifying $6-3(2x-2)$ .
(a) Expand and simplify the expression. (2)
(b) Find x when this expression is zero. (2)
Question 3Non-calculator · 7 marks
Answer each part.
(a) Show that $3(2n + 5) - 2(3n - 1)$ has the same value for every value of $n$ . (2)
(b) Factorise fully $18a^2b - 12ab^2$ (2)
(c) The area of a rectangle is $(10x^2 + 15x)\ \text{cm}^2$ . Its width is $5x$ cm. Find an expression for the perimeter of the rectangle. Give your answer in its simplest form. (3)

Answers and marks

(a) $5x + 20$

(b) $10y - 3$

(c) $3(2a + 5)$

(a) $12-6x$

(b) $2$

(a) It simplifies to $17$ .

(b) $6ab(3a - 2b)$

M1 Taking out a partial common factor such as $6a(3ab - 2b^2)$ or $2ab(9a - 6b)$ .
A1 The correct answer, $6ab(3a - 2b)$ .

(c) $(14x + 6)$ cm

Single brackets and common factors

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