Factorise completely the expression \((x + 2)^2\) - \((2x + 1)^2\)
MATHEMATICS
WAEC 2018
Factorise completely the expression
\((x + 2)^2\) - \((2x + 1)^2\)
- A. (3x + 2)(1 - x)
- B. (3x + 2)(2x + 1)
- C. 3(x+2)2
- D. 3(x + 1)(1 - x)
Correct Answer: D. 3(x + 1)(1 - x)
Explanation
\((x + 2)^2\) - \((2x + 1)^2\)
= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)
= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1
= -3 \(x^2 \) + 3
= 3 - 3 \(x^2 \)
= 3(1 - \(x^2 \))
= 3(1 + x)(1 - x)
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