1°) Développer:
(a + b) (c + d)
(a - b) (c + d)
(a + b) (c - d)
(a - b) (c - d)
2°) En déduire le développement de (a + b)² de (a - b)² et de (a + b) (a - b)
(a + b) (c + d)
= ac +ad +bc +bd
(a - b) (c + d)
=ac+ad-bc-bd(a + b) (c - d)
=ac-ad+bc-bd(a - b) (c - d)
=ac-ad-bc+bd (a + b)² = a² + 2ab + b² (a-b)² = a² - 2ab + b² (a+b)(a-b) = a² - b²1)
(a+b)(c+d)
a*c+a*d+b*c+b*d
ac+ad+bc+bd
(a-b)(c+d)
a*c+a*d-b*c-b*d
ac+ad-bc-bd
(a+b)(c-d)
a*c+a*(-d)+b*c+b*(-d)
ac-ad+bc-bd
(a-b)(c-d)
a*c+a*(-d)-b*c-b*(-d)
ac-ad-bc+bd
2)
(a+b)²
a²+2*a*b+b²
a²+2ab+b²
(a-b)²
a²+2*a*(-b)-b²
a²-2ab+b²
(a+b)(a-b)
a*a+a*(-b)+b*a+b*(-b)
a²-ab+ba-b²
a²-b²
