Question

Simplify the expression:

3² × [3x − (2y/3)]² − [2x − (5y/3)]²   

1. 45x2 + 16xy - 28y2
2. 17x2 + 96xy - 66y2 
3. 52x2 + 24xy - 75y2 
4. 45x2 + 96xy - 21y2 

Answer 1

Correct Answer - Option 4 : 45x2 + 96xy - 21y2 

32 × [3x − (2y/3)]2 − [2x − (5y/3)]2   

Formula used:

a² − b² = (a + b)(a - b)

(a - b)² = a² - 2ab + b²

Calculations:

= 32 × [(3x)2 + 3x × (2y/3) × 2 + (2y/3)2 ] - [ (2x)2 + 2x × (5y/3) × 2 + (5y/3)2]

= 32 × {9x2 + 4xy + (4y/9)2 - [ 4x2 - (20xy/3) + (25y2/9)]}

= 32 × [9x2 + 4xy + 4y2/9 - 4x2 + (20xy/3) - (25y2/9)]

= 32 × [5x2 + (32xy/3) - (21y2/9)]

= (45x2 + 96xy - 21y2)