Question

Formule:
(a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
(a+b)(a-b)=a²-b²

Calculați:
a). (2x-y)²-(x-2y)²
b). (a+b)²-(b+c)²
c). 49x²-(y+8x)²
d). (5a-3b)²-25a4; (25a4 = 25a la puterea 4)
e). (-2a²+3b)²-4a4; (4a4 = 4a la puterea 4)
f). b6 - (x-4b³)²; (b6 = b la puterea 6)

Answer 1

a). (2x-y)²-(x-2y)²=(2x-y+x-2y)(2x-y-x+2y)=(3x-3y)(x+y)=3(x-y)(x+y)
 b). (a+b)²-(b+c)²=(a+b+b+c)(a+b-b-c)=(a+2b+c)(a-c)
 c). 49x²-(y+8x)²=(7x+y+8x)(7x-y-8x)=(15x+y)(-x-y)
 d). (5a-3b)²-25a⁴=(5a-3b+5a²)(5a-3b-5a²)
e). (-2a²+3b)²-4a⁴=(-2a²+3b+2a²)(-2a²+3b-2a²)=3b(-4a²+3b)
 f). b⁶ - (x-4b³)²=(b³+x-4b³)(b³ - x+4b³)=(x-3b³)(5b³ - x)=