Question

What is the sum of $l^2$ + $m^2$, $m^2$ + $n^2$, and $n^2$ + $l^2$?

• A. $l^4$ + $m^4$ + $n^4$
• B. $l$ + $m$ + $n$
• C. 2($l^2$ + $m^2$ + $n^2$)
• D. $l^2$ + $m^2$ + $n^2$

Answer 1

The correct option is C 2($l^2$ + $m^2$ + $n^2$)

The given polynomials are
𝑙${}^2$ + 𝑚${}^2$, 𝑚${}^2$ + 𝑛${}^2$, and 𝑛${}^2$ + 𝑙${}^2$.
Required sum = 𝑙${}^2$ + 𝑚${}^2$ + 𝑚${}^2$ + 𝑛${}^2$ + 𝑛${}^2$ + 𝑙${}^2$
= 𝑙${}^2$ + 𝑙${}^2$ + 𝑚${}^2$ + 𝑚${}^2$ + 𝑛${}^2$ + 𝑛${}^2$
= 2𝑙${}^2$ + 2𝑚${}^2$ + 2𝑛${}^2$
= 2($l^2$ + $m^2$ + $n^2$)