Question

Show that (x+5)^2-(x-5)^2=20x

Answer 1

See Explanation

Explanation:

`formula \: to \: be \: used: \\ \boxed{ \boxed{ {a}^(2) - {b}^(2) = (a + b)(a - b)}} \\ \\ {(x + 5)}^(2) - {(x - 5)}^(2) \\ \\ = \{(x + 5) + (x - 5) \} \{(x + 5) - (x - 5) \} \\ \\ = \{x + \cancel5 + x -\cancel 5 \} \{\cancel x + 5 - \cancel x + 5 \} \\ \\ = \{2x \} \{10 \} \\ \\ = 20x \\ \\ \therefore \: {(x + 5)}^(2) - {(x - 5)}^(2) = 20x \\ thus \: proved`