ABC26GN0993 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:
If $(a+b+2 c+3 d)(a-b-2 c+3 d)=(a-b+2 c-3 d)$ $(a+b-2 c-3 d)$, then $2 b c$ is equal to
(a)$\frac{3}{2}$
(b)$\frac{3 a}{2 d}$
(c)3ad
(d)$a^{2} d^{2}$
Answer
Explanation
$(a+b+2 c+3 d)(a-b-2 c+3 d)$ $$=(a-b+2 c-3 d)(a+b-2 c-3 d) \begin{gathered} \Rightarrow[(a+b)+(2 c+3 d)][(a-b)-(2 c-3 d)] \\ \quad=[(a-b)+(2 c-3 d)][(a+b)-(2 c+3 d)] \end{gathered} \begin{aligned} \Rightarrow & (a+b)(a-b)-(a+b)(2 c-3 d)+(a-b)(2 c+3 d) \\ & -(2 c+3 d)(2 c-3 d) \\ = & (a-b)(a+b)-(a-b)(2 c+3 d)+(a+b)(2 c-3 d) \\ & -(2 c+3 d)(2 c-3 d) \end{aligned} \Rightarrow(a+b)(2 c-3 d)=(a-b)(2 c+3 d)$$ $\Rightarrow 2 a c-3 a d+2 b c-3 b d=2 a c+3 a d-2 b c-3 b d$ $$\Rightarrow 4 b c=6 a d \Rightarrow 2 b c=3 a d .$$
Explanation as extracted from the printed page; notation may be imperfect.
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