Question

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

Answer 1

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

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Answer 2

Answer:

Let's simplify step-by-step.

(a−b)(a+b)+b−c+(b−c)(b+c)+(c−a)(c+a)

Distribute:

=(a)(a)+(a)(b)+(−b)(a)+(−b)(b)+b+−c+(b)(b)+(b)(c)+(−c)(b)+(−c)(c)+(c)(c)+(c)(a)+(−a)(c)+(−a)(a)

=a2+ab+−ab+−b2+b+−c+b2+bc+−bc+−c2+c2+ac+−ac+−a2

Combine Like Terms:

=a2+ab+−ab+−b2+b+−c+b2+bc+−bc+−c2+c2+ac+−ac+−a2

=(a2+−a2)+(ab+−ab)+(ac+−ac)+(−b2+b2)+(bc+−bc)+(−c2+c2)+(b)+(−c)

=b+−c

Answer:

=b−c

Explanation:

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