Question

if m = -2 and n = 2 find the value of m2 + n2 - 2mn

Answer 1

Given: Equation - m² + n² - 2mn & The values of m & n I.e -2,2.

Need to find: The value of m² + n² - 2mn?

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's apply the given values & find the value of m² + n² - 2mn.

⠀⠀⠀⠀⠀

As we know that,

⠀⠀⠀⠀⠀

$\begin{gathered}\star\:{\underline{\boxed{\frak{m = -2, n = 2}}}}\\\\\\ \: \: \: \: \: \: \bf{\dag}\:{\underline{\frak{ Putting\:given\:values\:,}}}\\\\\\ :\implies\sf {m}^{2} + {n}^{2} - 2mn \\\\\\ :\implies\sf { - 2}^{2} + {2}^{2} - 2 \times - 2 \times 2 \\\\\\ :\implies\sf - 4 + 4 - ( - 4) \times 2\\\\\\ :\implies\sf - 4 + 4 - ( - 8)\\\\\\ :\implies\sf - ( - 8)\\\\\\ :\implies{\underline{\boxed{\frak{\purple{8}}}}}\:\bigstar\\\\\end{gathered}$

⠀⠀⠀⠀⠀

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Therefore,

⠀⠀⠀⠀⠀

The value of m² + n² - 2mn, 8.

⠀⠀⠀⠀⠀

$\therefore {\underline{\sf Hence, The \: value \: of \: {\bf{m^{2} + n^{2}- 2mn} } \:{ \sf if \: }{\bf m = -2, n = 2} \: is \: {\bf{8}}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

★ More to know:

★ Variable: A variable is an alphabet used in mathematical expression. The most common variables used are x & y.

★ Constant: A number is also called as a constant. Example - 4, 5, 8 etc..!

Answer 2

m² + n² - 2mn

= (m - n)²

{as (a² + b² - 2ab) = (a - b)²}

∴ (m - n)²

= [(- 2) - (2)]²

= (- 4)²

= 16.

∴ The value of m² + n² - 2mn is 16 if m = (- 2) and n = 2.