Question
(a) Factorise completely.
18x² – 12x
(b) Expand and simplify.
(x + 5)(x – 3)
▶️ Answer/Explanation
Solution
Ans:
(a) 6x(3x – 2) (take out common factor 6x)
(b) x² + 2x – 15 (use FOIL method: x×x + x×(-3) + 5×x + 5×(-3))
Question
The diagram shows a rectangle with length \(3x-12\) and width \(x+7\).
Find an expression for the perimeter of the rectangle.
Give your answer in its simplest form.
▶️ Answer/Explanation
Solution
Ans: \(8x-10\) or \(2(4x-5)\)
The perimeter \( P \) of a rectangle is calculated using the formula:
\[ P = 2(\text{Length} + \text{Width}) \]
Substitute the given expressions for length (\(3x – 12\)) and width (\(x + 7\)):
\[ P = 2((3x – 12) + (x + 7)) \]
Simplify the expression inside the parentheses:
\[ P = 2(4x – 5) \]
Finally, expand to get the simplest form:
\[ P = 8x – 10 \]