MCQ
The expression $(3 a+2 b+3 c)^2-(2 a+3 b+2 c)^2+5 b^2$ is perfect square of the expression
- A$\sqrt{5}(a+b+c)$
- B$\sqrt{5}(a+b)$
- ✓$\sqrt{5}(a+c)$
- D$\sqrt{5}(a+c-b)$
✓
Answer
Correct option: C.
$\sqrt{5}(a+c)$
(c)
$(3 a+2 b+3 c)^2-(2 a+3 b+2 c)^2+5 b^2$
$=(3 a+2 b+3 c+2 a+3 b+2 c)(3 a+2 b+3 c-2 a-3 b-2 c)+5 b^2$
$=(5 a+5 b+5 c)(a-b+c)+5 b^2=5|(a+c)+b|\left\{(a+c)-b \mid+5 b^2\right.$
$=5\left\{(a+c)^2-b^2\right\}+5 b^2=5(a+c)^2=\{\sqrt{5}(a+c)\}^2$
$(3 a+2 b+3 c)^2-(2 a+3 b+2 c)^2+5 b^2$
$=(3 a+2 b+3 c+2 a+3 b+2 c)(3 a+2 b+3 c-2 a-3 b-2 c)+5 b^2$
$=(5 a+5 b+5 c)(a-b+c)+5 b^2=5|(a+c)+b|\left\{(a+c)-b \mid+5 b^2\right.$
$=5\left\{(a+c)^2-b^2\right\}+5 b^2=5(a+c)^2=\{\sqrt{5}(a+c)\}^2$
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