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Simplify and factorise (a+b+c)^2-(a-b-c)^2+4b^2-4c^2

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Simplify and factorise (a+b+c)^2-(a-b-c)^2+4b^2-4c^2

Posted by Palak Gaba 6 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 6 years, 10 months ago

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Consider, (a+b+c)² – (a – b – c)²+ 4b²– 4c²
= a² + b² + c² + 2ab + 2bc + 2ca – (a² + b² + c²– 2ab + 2bc – 2ca)+ 4b²– 4c²
= a² + b² + c²+ 2ab + 2bc + 2ca – a² – b² – c² + 2ab – 2bc +2ca + 4b²– 4c²
= 4ab + 4ca + 4b²– 4c²
= 4(ab + ca + b²– c²)
= 4[a(b + c) +(b²– c²)]
= 4[a(b + c) + (b + c)(b – c)]
= 4(b + c)(a + b – c)

2Thank You

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