Simplify the given expression.

​$$\frac{140 \times 140 + 280 \times 450 \div 3 + 150 \times 150}{290}$$​​

Correct option is B

Given:

​$$\frac{140 \times 140 + 280 \times 450 \div 3 + 150 \times 150}{290}$$​​

Formula Used:

​$$\begin {array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​

Solution:

​$$\frac{140 \times 140 + 280 \times 450 \div 3 + 150 \times 150}{290}$$​​

​$$\frac{140 \times 140 + 280 \times 150 + 150 \times 150}{290}$$​​

​$$\frac{19600 + 42000 + 22500}{290}$$​​

​$$\frac{19600 + 42000 + 22500}{290}$$​​

​$$\frac{84100}{290}$$​​

= 290 

Alternate Method: ​

Formula - $$(a+b)^2 = a^2 +b^2+2ab$$ 

​$$=\frac{140 \times 140 + 280 \times 450 \div 3 + 150 \times 150}{290} \\ \ \\ = \frac{140 \times 140 +2 \times 140 \times 150 + 150 \times 150}{290}\\ \ \\ = \frac{(140+150)^2}{290} \\ \ \\ = \frac{(290)^2}{290} \\ \ \\ = \frac{290 \times 290}{290} \\ \ \\ = 290$$​​