CHRISTELLE40
Answered

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)

Sagot :

(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 - b²    
QUEENOMEGA

1)

 

(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