Simplifying Expression Using BODMAS Rule

The problem requires simplifying the expression $\frac{7}{9} \times \frac{21}{5} \times 25 (65^2 - 55^2)$ using the BODMAS rule.

BODMAS stands for: Bracket, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.

Step-by-Step Simplification

Step 1: Simplify the expression within the brackets (Orders).

Calculate the term involving powers and subtraction: $(65^2 - 55^2)$.

Using the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$:

$65^2 - 55^2 = (65 - 55)(65 + 55)$

$= (10)(120)$

$= 1200$

Step 2: Substitute the bracket result back into the expression.

The expression becomes:

$\frac{7}{9} \times \frac{21}{5} \times 25 \times 1200$

Step 3: Perform Multiplication from left to right.

First, multiply the fractions:

$\frac{7}{9} \times \frac{21}{5} = \frac{7 \times 21}{9 \times 5}$

Simplify by dividing 21 and 9 by their common factor 3:

$= \frac{7 \times (3 \times 7)}{(3 \times 3) \times 5} = \frac{7 \times 7}{3 \times 5} = \frac{49}{15}$

The expression is now:

$\frac{49}{15} \times 25 \times 1200$

Next, multiply $\frac{49}{15}$ by 25:

$\frac{49}{15} \times 25 = \frac{49 \times 25}{15}$

Simplify by dividing 25 and 15 by their common factor 5:

$= \frac{49 \times (5 \times 5)}{(3 \times 5)} = \frac{49 \times 5}{3} = \frac{245}{3}$

The expression is now:

$\frac{245}{3} \times 1200$

Finally, multiply $\frac{245}{3}$ by 1200:

$\frac{245}{3} \times 1200 = 245 \times \frac{1200}{3}$

Simplify by dividing 1200 by 3:

$= 245 \times 400$

Step 4: Calculate the final product.

$245 \times 400 = 98000$

Final Answer

The simplified value of the expression is 98000.