Question:
\[ 75 \times 75 + 2 \times 75 \times 25 + 25 \times 25 \] is equal to
(a) 10000
(b) 6250
(c) 7500
(d) 3750
Solution:
Using identity:
\[ a^2+2ab+b^2=(a+b)^2 \]
Here,
\[ a=75,\quad b=25 \]
Therefore,
\[ 75^2+2(75)(25)+25^2 = (75+25)^2 \]
\[ =100^2 \]
\[ =10000 \]
Hence, the correct answer is:
\[ \boxed{10000} \]