Worksheets · Foundation and Higher

Expanding two binomials

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

Question 1Non-calculator · 4 marks
Expand and simplify each expression.
(a) Expand and simplify $(x + 3)(x + 5)$ (2)
(b) Expand and simplify $(x - 4)(x + 2)$ (2)
Question 2Non-calculator · 3 marks
Expand and simplify each product.
(a) Expand and simplify $(2x - 3)(x + 4)$ . (2)
(b) Expand and simplify $(3 - x)(3 + x)$ . (1)
Question 3Non-calculator · 6 marks
A square has sides of length $(x + 3)$ cm. A rectangle has length $(x + 7)$ cm and width $(x - 1)$ cm, where $x > 1$ .
(a) Prove that the area of the square is always $16\ \text{cm}^2$ more than the area of the rectangle. (3)
(b) The area of the rectangle is $20\ \text{cm}^2$ . Find the length of a side of the square. (3)

Answers and marks

(a) $x^2 + 8x + 15$

(b) $x^2 - 2x - 8$

(a) $2x^{2}+5x-12$

(b) $9-x^{2}$

(a) $(x^2 + 6x + 9) - (x^2 + 6x - 7) = 16$

(b) $6$ cm

Expanding two binomials

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