Question

factorise the following using suitable idintities (a+b+c)²-(a+b-c)²​

Answer 1

Answer:

$\mathrm{\left(a+b+c\right)^2-\left(a+b-c\right)^2=4ac+4bc}$

Step-by-step explanation:

$\mathrm{\left(a+b+c\right)^2-\left(a+b-c\right)^2}$

$\mathrm{\left(a+b+c\right)^2=\left(a+b+c\right)\left(a+b+c\right)}$

$\mathrm{=\left(a+b+c\right)\left(a+b+c\right)-\left(a+b-c\right)^2}$

$\mathrm{\left(a+b-c\right)^2=\left(a+b-c\right)\left(a+b-c\right)}$

$\mathrm{=\left(a+b+c\right)\left(a+b+c\right)-\left(a+b-c\right)\left(a+b-c\right)}$

$\mathrm{=2ab+2ac+a^2+b^2+2bc+c^2-\left(a+b-c\right)\left(a+b-c\right)}$

$\mathrm{=2ab+2ac+a^2+b^2+2bc+c^2-2ab+2ac-a^2-b^2+2bc-c^2}$

$\mathrm{=4ac+4bc}$