Simplify
\[ 175 \times 175 + 2 \times 175 \times 25 + 25 \times 25 \]
Solution:
Using identity:
\[ a^2 + 2ab + b^2 = (a+b)^2 \]
\[ 175 \times 175 + 2 \times 175 \times 25 + 25 \times 25 \]
\[ = (175)^2 + 2(175)(25) + (25)^2 \]
\[ = (175 + 25)^2 \]
\[ = (200)^2 \]
\[ = 40000 \]