Simplify the given term ${(a + b + c)}^{2} - {(a - b - c)}^{2} + 4 b^{2} - 4 c^{2}$

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Solution

The given expression $(a + b + c)^{2} - (a - b - c)^{2} + 4 b^{2} - 4 c^{2}$ can be solved as shown below:

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

Hence, $(a + b + c)^{2} - (a - b - c)^{2} + 4 b^{2} - 4 c^{2} = 4 (b + c) (a + b - c)$ .

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Similar questions

Simplify and factorise (a + b + c)² - (a - b - c)² + 4b² - 4c²

Factorize :

(a + b + c)²- ( a- b - c)² + 4b²- 4c²

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

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

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

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