Question

factorise a2+b2+2ab-c2​

Answer 1

Answer:

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$To\ factorise-{a}^{2}+{b}^{2}+2ab-{c}^{2}$

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• ${(a+b)}^{2}={a}^{2}+{b}^{2}+2ab$
• ${a}^{2}-{b}^{2}=(a-b)(a+b)$

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${a}^{2}+{b}^{2}+2ab-{c}^{2}$

$=>[{a}^{2}+{b}^{2}+2ab]-[{c}^{2}]$

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

$=>(a+b-c)(a+b+c)$

Answer 2

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$\sf{\green{Formula\:used;}}$

$\sf{(a+b)^{2}\:=\:a^2\:+\:b^2\:+\:2ab}$

$\sf{ {a}^{2}\:-\:{b}^{2}\:=\:(a−b)(a+b)}$

$\sf{\green{Solution;}}$

$\implies{\sf{ {a}^{2}+{b}^{2}+2ab-{c}^{2}a2+b2+2ab−c2}}$

$\implies{\sf{ [{a}^{2}+{b}^{2}+2ab]-[{c}^{2}]\\ [a2+b2+2ab]−[c2]\\ (a+b-c)(a+b+c)=>(a+b−c)(a+b+c)}}}$