Réponse :
Factoriser
A = (x²+xy)²-(x²-xy-2y²)² identité remarquable a²-b²=(a+b)(a-b)
= (x²+ xy + x² - xy -2y²)(x²+xy - x² + xy + 2y²)
= (2x²- 2y²)(2y² + 2xy)
= 4(x² - y²)(y² + xy)
= 4y(x²-y²)(y + x)
= 4y(x + y)(x - y)(y+x)
= 4y(x-y)(x+y)²
B = (2 x² - 18)(x-2) - (x²-9)(2 x - 1) + 3 - x
= 2(x² - 9)(x-2) - (x² - 9)(2 x - 1) - (x - 3)
= 2(x - 3)(x+3)(x-2) -(x-3)(x+3)(2 x - 1) - (x-3)
= (x-3)[2(x+3)(x-2) -(x+3)(2x -1) - 1]
= (x-3)[2(x² + x - 6) -(2 x²+5 x - 3) - 1]
= (x-3)[2 x² + 2 x - 12 - 2 x² - 5 x + 3 - 1]
= (x-3)(- 3 x - 10)
C = 16 x² - 9 + (4 x+3)(x-1) + 5 x(x-2) - 4(x-2)
= (4 x + 3)(4 x - 3) + (4 x + 3)(x - 1) + 5 x(x-2) - 4(x-2)
= (4 x +3)[4 x - 3 + x - 1 + 5 x² - 10 x - 4 x + 8]
= (4 x + 3)[5 x² - 9 x + 4]
Explications étape par étape
