Factorization Of Algebraic Expressions — Maths STD 9 — Question
Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions3 Marks
Question
Factorize:
$(a - b + c)^2 + (b - c + a)^2 + 2(a - b + c)(b - c + a)$
✓
Answer
$(a - b + c)^2 + (b - c + a)^2 + 2(a - b + c)(b - c + a)$
$Let (a - b + c) = x and (b - c + a) = y = x^2 + y^2 + 2xy$
Using the identity $(a + b)^2 = a^2 + b^2 + 2ab = (x + y)^{2}$
Now, substituting $x$ and $y$ $(a - b + c + b - c + a)^2$
Cancelling $-b, +b + c, -c = (2a)^2 = 4a^2$
$\therefore$ $(a - b + c)^2 + (b - c + a)^2 + 2(a - b + c)(b - c + a) = 4a^2$
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