Question

Show that:-
(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

Answer 1

Step-by-step explanation:

Question -

Show that:-

(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

ㅤ

Solution -

➠ㅤTo prove whether the above equation is equals to 0, we'll simplify it.

ㅤ

$\red{➠}$(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

$\red{➠}${(a – b) (a + b)} + {(b – c) (b + c)} + {(c – a) (c + a)} = 0

ㅤ

Formula to be used -

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

ㅤ

$\red{➠}$$(a - b {)}^{2} + (b - c {)}^{2} + (c - a {)}^{2} = 0 \\ \\ {(a)}^{2} - (b {)}^{2} + {(b)}^{2} - {(c)}^{2} + {(c)}^{2} - {(a)}^{2} = 0 \\ \\ 0 = 0$

Hence proved.