Question

simplify (a+b+c)(a+b-c)​

Answer 1

Solution :

$\bf (a+b+c)(a+b-c)$

$\bf : \implies a(a+b-c) + b(a+b-c) + c(a+b-c)$

$\bf : \implies (a^{2} + ab - ac) + (ab +b^{2} -bc) + (ac+bc - c^{2})$

$\bf : \implies a^{2} + ab - ac + ab +b^{2} -bc + ac+ bc - c^{2}$

$\bf : \implies a^{2} +b^{2} - c^{2} + ab + ab - ac + ac - bc + bc$

$\bf : \implies a^{2} +b^{2} - c^{2} + 2ab$

$\bf Hence, \: (a + b + c)(a + b - c) = a^{2} + b^{2} - c^{2} + 2ab$

Answer 2

$\huge\tt{\underline{\underline{\star{\red{Question:}}}}}$

Simplify : ( a + b + c) ( a + b - c)

$\huge\mathtt{\underline{\underline{\star{\red{Solution:}}}}}$

(a + b + c) (a + b - c)

$: \implies$ a( a + b - c) + b( a + b - c) + c( a + b - c)

$:\implies$ a² + ab - ac + ab + b² - bc + ca + bc - c²

$:\implies$ a² + b² - c² + ab + ab + bc - bc + ca - ca

$:\implies$ a² + b² - c² + 2ab

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