Question

1 – Desenvolva os produtos notáveis a seguir:
a) (x + 1)(x + 3)
b) (x + 2)(x – 5)
c) (x – 4)(x – 2)
d) (x – 6)(x + 3)
e) (x + y)³ f) (x – y)³
g) (x + 4)³
h) (2y – 1)³
i) (2a + 1)³

Answer 1

Resposta:

a)

R:x²+4x+3

b)

R:

x²-3x-10

c)

R:x²-6x-8

d)

R:x²-3x+18

e)

R:x³+3x²y+3xy²+y³

f)

R:x³-3x²y-3xy²-y³

g)

R:x³+12x²+48x+64

h)

R:8y³-12y²-4y-1

i)

R:8a³+12a²+6a+1

Explicação passo-a-passo:

a) (x+1)(x+3)

x²+x+3x+3

x²+4x+3

b)(x+2)(x-5)

x²-5x+2x-10

x²-3x-10

c)(x-4)(x-2)

x²-2x-4x+8

x²-6x-8

d)(x-6)(x+3)

x²+3x-6x-18

x²-3x+18

e)(x+y)³

(x+y)(x+y)(x+y)

(x²+xy+xy+y²)(x+y)

x³+x²y+x²y+xy²+x²y+xy²+xy²+y³

x³+3x²y+3xy²+y³

f)(x-y)³

(x-y)(x-y)(x-y)

(x²-xy-xy-y²)(x-y)

x³-x²y-x²y-xy²-x²y-xy²-xy²-y³

x³-3x²y-3xy²-y³

g)(x+4)³

(x+4)(x+4)(x+4)

(x²+4x+4x+16)(x+4)

x³+4x²+4x²+16x+4x²+16x+16x+64

x³+12x²+48x+64

h)(2y-1)³

(2y-1)(2y-1)(2y-1)

(4y²-2y-2y+1)(2y-1)

8y³-4y²-4y²-2y-4y²-2y-2y-1

8y³-12y²-6y-1

i)(2a+1)³

(2a+1)(2a+1)(2a+1)

(4a²+2a+2a+1)(2a+1)

8a³+4a²+4a²+2a+4a²+2a+2a+1

8a³+12a²+6a+1