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Algebraic Identities

Factorise: a-...

Question

Factorise:

$(a - b + c)^{2} + (b - c + a)^{2} + 2 (a - b + c) (a - c + a)$

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Solution

$(a - b + c)^{2} + (b - c + a)^{2} + 2 (a - b + c) (a - c + a) {∵ a^{2} + b^{2} + 2 a b = (a + b^{2})} = [a - b + c + b - c + a]^{2} = (2 a)^{2} = 4 a^{2}$

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Similar questions

Q. Factorize:

(a − b + c)² + (b − c + a)² + 2(a − b + c) (b − c + a)

Q. If a² + b² + c² + ab + bc + ca = 89 and (a + b) : (b + c) : (c + a) = 12 : 5 : 3, where a, b and c are real numbers, then (a² + b² + c² – ab – bc – ca) equals

यदि a² + b² + c² + ab + bc + ca = 89 तथा (a + b) : (b + c) : (c + a) = 12 : 5 : 3, जहाँ a, b व c वास्तविक संख्याएँ हैं, तब (a² + b² + c² – ab – bc – ca) बराबर है

(a^{2} - 2 b c - b^{2} - c^{2}) \div (a - b - c) (a + b + c)

a² + b² + c² - ab - bc - ca equals:

Q. The simplified value of the experession

{(a + b - c)}^{2} + 2 (a + b - c) (a - b + c) + {(a - b + c)}^{2}

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