verify that (11pq +4q) ^2 - (11pq-4q) ^2 =176pq ^2
Answers
Given:
An equation (11p q + 4q)² - (11p q - 4q)² = 176 p q².
To Find:
The proof/ verification of the above equation.
Solution:
The given problem can be solved using the expansions of the forms (a+b)², and (a-b)².
1. The given equation is (11-p q + 4q)² - (11-p q - 4q)² = 176 p q².
2. Consider the formulas (a+b)², and (a-b)². They are formulated as,
- (a+b)² = a² + b² + 2ab,
- (a-b)² = a² + b² - 2ab.
3. Using the above formulae, expand the LHS of the given equation,
=> ( 121 p²q² + 16q² + 88pq² ) - ( 121 p²q² + 16q² - 88pq² ),
=> 121 p²q² + 16q² + 88pq² - 121 p²q² - 16q² + 88pq², ( solve the equations by subtracting like terms),
=> 0 + 0 + 176 pq²,
=> 176 pq² which is equal to the value of the RHS.
Hence, equality is proved.
Therefore, the equation (11-p q + 4q)² - (11-p q - 4q)² = 176 pq² is correct and verified.