Question

Desenvolva os produtos notaveis a seguir

a) (2x + y)²

b) (a + 2b)²

c) (5 - y)²

d) (2a - 2)²

e) (a + b)(a - b)

f) ( 2x + 4)(2x - 4)

Answer 1

a) (2x + y)²
(2x + y) (2x + y)
4x²+2xy+2xy+y²
4x²+4xy+y²

b) (a + 2b)²
(a + 2b) (a + 2b)
a²+2ab+2ab+ 4b²
a²+4ab+ 4b²

c) (5 - y)²
(5 - y) (5 - y)
5²-5y-5y+y²
5²-10xy+y²
25-10xy+y²

d) (2a - 2)²
(2a - 2) (2a - 2)
4a²-2a-2a+4
4a²-4a+4

e) (a + b)(a - b)
a²-ab+ab-b²
a²-b²

f) ( 2x + 4)(2x - 4)
4x²-8x+8x-16
4x²-16

Answer 2

a) (2x + y)² = (2x)² + 2.2x.y + y² = 4x² + 4xy + y²

b) (a + 2b)² = a² + 2.a.2b + (2b)² = a² + 4ab + 4b²

c) (5 - y)² = 5² - 2.5y + y² = 25 - 10y + y² = y² - 10y + 25

d) (2a - 2)² = (2a)² - 2.2.2a + 2² = 4a² - 8a + 4

e) (a + b)(a - b) = a² - ab + ab - b.b = a² - b²

f)
= ( 2x + 4).(2x - 4)

= (2x)² - 4.2x + 4.2x + 4.(-4)

= 4x² - 8x + 8x - 16

= 4x² - 16