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Algebraic Identities — Maths STD 9 — Question

CBSE BoardEnglish MediumSTD 9MathsAlgebraic Identities1 Mark
MCQ
The expression $(4 a+5 b+5 c)^2-(5 a+4 b+4 c)^2+9 a^2$ is a perfect square of the expression
  • A
    $\sqrt{3}(b+c)$
  • B
    $3(b+c-a)$
  • ✓
    $3(b+c)$
  • D
    $3(-b+c-a)$
✓

Answer

Correct option: C.
$3(b+c)$
(c)
$(4 a+5 b+5 c)^2-(5 a+4 b+4 c)^2+9 a^2$
$=(4 a+5 b+5 c+5 a+4 b+4 c)(4 a+5 b+5 c-5 a-4 b-4 c)+9 a^2$
$=9(a+b+c)(-a+b+c)+9 a^2$
$=9\{(b+c)+a\}\{(b+c)-a\}+9 a^2=9\left\{(b+c)^2-a^2\right\}+9 a^2=9(b+c)^2=\{3(b+c)\}^2$

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