Bonjour !
a. (a + b)²+ (a - b)² = 2(a² + b²)
(a + b)²+ (a - b)² =
= a² + 2ab b² + a² - 2ab + b²
= a²+ b² + a² + b²
= 2a² + 2b²
=2(a² + b²)
b. 4ab = (a + b)² -(a- b)²
(a + b)² - (a- b)² =
= a² + 2ab + b² - (a² - 2ab + b² )
= a² + 2ab + b² - a² + 2ab - b²
= 2ab + 2ab
= 4ab
c. (a + b)(a - b) + b² = ab+a(a-b)
(a + b)(a - b) + b² =
= a² - b² + b²
= a²
ab+a(a-b) =
= ab + a² - ab
= a²
Donc (a + b)(a - b) + b² = ab+a(a-b) (même résultat à la simplification)