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

1.	Simplify :- (a-b)(a+b)+(b-c)+(b-c)(b+c)+(c-a)(c+a)
Answer» Explanation: $(a-b)(a+b)+(b-c)+(b-c)(b+c)+(c-a)(c+a)\\$ = $a^{2}-b^{2}+b-c+b^{2}-c^{2}+c^{2}-a^{2}$ {Since, (x+a)(x-a)=x²-a²} = $a^{2} -a^{2} +b^{2}-b^{2}+c^{2}-c^{2}+b-c$ {LIKE terms cancel each other} = $0+0+0+b-c$ = $b-c$ HENCE, $(a-b)(a+b)+(b-c)+(b-c)(b+c)+(c-a)(c+a)\\$ = $b-c$ REMARKS: The answer is 100% correct. MARK as BRAINLIEST if your doubt is cleared. Have a phenomenal future! JAI HIND

Answer»

Explanation:

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