Question

Simplify: ( x + 2y )2 - ( x - 2y ) 2​

Answer 1

(x + 2y)²- (x - 2y)²

= (x² + 2×x×2y + 4y²)-(x² - 2×x×2y + 4y²)

= (x² + 4xy + 4y²)-(x² - 4xy + 4y²)

= x² + 4xy + 4y² - x² + 4xy - 4y²

= (x² - x²) + (4xy + 4xy) + (4y² - 4y²)

= 0 + 8xy + 0

= 8xy

Hence, (x + 2y)²- (x - 2y)² = 8xy.