Question

Utilizando A regra dos produtos notáveis,calcule:

Answer 1

Olá...

1ª Parte

a)

(p + a)²

(p + a).(p + a)

p² + pa + pa + a²

p² + 2pa + a²

b)

(c + d)²

(c + d).(c + d)

c² + cd + cd + d²

c² + 2cd + d²

c)

(r + s)²

(r + s).(r + s)

r² + rs + rs + s²

r² + 2rs + s²

d)

( t + u)²

(t + u).(t + u)

t² + tu + tu + u²

t² + 2tu + u²

e)

(8 + 2)²

(8 + 2).(8 + 2)

64 + 16 + 16 + 4

64 + 32 + 4

100

f)

(5 + 3)²

(5 + 3).(5 + 3)

25 + 15 + 15 + 9

25 + 30 + 9

64

g)

(4 + 5)²

(4 + 5).(4 + 5)

16 + 20 + 20 + 25

81

h)

(3 + 1)²

(3 + 1).(3 + 1)

9 + 3 + 3 + 1

16

2ª Parte:

i)

(5x + 3y)²

(5x + 3y).(5x + 3y

25x² + 15xy + 15xy + 9y²

25x² + 30xy + 9y²

j)

(6a + 3b)²

(6a + 3b).(6a + 3b)

36a² + 18ab + 18ab + 9b²

36a² + 36ab + 9b²

k)

(3m + 6n)²

(3m + 6n).(3m + 6n)

9m² + 18mn + 18mn + 36n²

9m² + 36mn + 36n²

l)

(2b + 5c)²

(2b + 5c).(2b + 5c)

4b² + 10bc + 10bc + 25c²

4b² + 20bc + 25c²

Espero ter ajudado.

Answer 2

Resposta:

A)

$(p + a) {}^{2} = {p}^{2} + 2.p.a + {a}^{2}$

B)

$(c + d) {}^{2} = {c}^{2} + 2.c.d + {d}^{2}$

C)

$( r + s) {}^{2} = {r}^{2} + 2.r.s + {s}^{2}$

D)

$(t + u) {}^{2} = {t}^{2} + 2.t.u + {u}^{2}$

E)

$(8 + 2) {}^{2} = {8}^{2} + 2.8.2 + {2 }^{2} \\ 64 + 32 + 4 = 100$

F)

$(5 + 3) {}^{2} = {5}^{2} + 2.5.3 + {3}^{2} = 25 + 30 + 9 = 64$

G)

$(4 + 5) {}^{2} = {4}^{2} + 2.4.5 + {5}^{2} = 16 + 40 + 25 = 81$

H)

$(3 + 1) {}^{2} = {3}^{2} + 2.3.1 + {1}^{2} = 9 + 6 + 1 = 16$

I)

$(5x + 3y) {}^{2} = ( {5x})^{2} + 2.5x.3y + {( 3y})^{2} \\ 25 {x}^{2} + 30xy + 9 {y}^{2}$

J)

$(6a + 3b) {}^{2} = (6a) {}^{2} + 2.6a.3b + (3b) {}^{2} = 36 {a}^{2} + 36ab + 9 {b}^{2}$

K)

$(3m + 6n) {}^{2} = (3m) {}^{2} + 2.3m.6n + (6n) { }^{2} = \\ 9 {m}^{2} + 36mn + 36 {n}^{2}$

L)

$(2b + 5c) {}^{2} = (2b) {}^{2} + 2.2b.5c + (5c) {}^{2} \\ 4 {b}^{2} + 20bc + 25 {c}^{2}$