Question

1)Efetue :
a) ( 2 x³ - 5 )² =
b) ( 8 x - 7 a )² =
c) ( 6 - a³ ) =
d) ( 3 a² + 1 )² =
e) ( 10 p + 3 q )² =
f) ( 1 + pq )² =
g) ( x + 1 / 3 )² =
h) ( b + 3 / 4 )² =

2) A expressão ( x - y )² - ( x + y )² é equivalente a :
a) 0 ( )
b) 2y² ( )
c) - 2y² ( )
d) - 4 x y ( )

3) A expressão ( 2 a + b)² - ( a - b )² é igual a :
a) 3 a² + 2 b² ( )
b) 3 a² + 6 a b ( )
c) 4 a² b + 2 a b² ( )
d) 4 a² + 4ab + b² ( )

Answer 1

Oie, Td Bom?!

1.

a)

$= (2x {}^{3} - 5) {}^{2}$

$= (2x {}^{3} ) {}^{2} - 2 \: . \: 2x {}^{3} \: . \: 5 + 5 {}^{2}$

$= 4x {}^{6} - 20x {}^{3} + 25$

b)

$= (8x - 7a) {}^{2}$

$= (8x) {}^{2} - 2 \: .\: 8x \: . \: 7a + (7a) {}^{2}$

$= 64x {}^{2} - 112ax + 49a {}^{2}$

c)

$= (6 - a {}^{3} ) {}^{2}$

$= 6 {}^{2} - 2 \: . \: 6a {}^{3} + (a {}^{3} ) {}^{2}$

$= 36 - 12a {}^{3} + a {}^{6}$

$= a {}^{6} - 12a {}^{3} + 36$

d)

$= (3a {}^{2} + 1) {}^{2}$

$= (3a {}^{2} ) {}^{2} + 2 \: . \: 3a {}^{2} \: . \: 1 + 1 {}^{2}$

$= 9a {}^{4} + 6a {}^{2} + 1$

e)

$= (10p + 3q) {}^{2}$

$= (10p) {}^{2} + 2 \: . \: 10p \: . \: 3q + (3q) {}^{2}$

$= 100p {}^{2} + 60pq + 9q {}^{2}$

f)

$= (1 + pq) {}^{2}$

$= 1 {}^{2} + 2 \: . \: 1pq + (pq) {}^{2}$

$= 1 + 2pq + p {}^{2} q {}^{2}$

g)

$= (x + \frac{1}{3} ) {}^{2}$

$= x {}^{2} + 2x \: . \: \frac{1}{3} + ( \frac{1}{3} ) {}^{2}$

$= x {}^{2} + \frac{2}{3} x + \frac{1}{9}$

h)

$= (b + \frac{3}{4} ) {}^{2}$

$= b {}^{2} + 2b \: . \: \frac{3}{4} + ( \frac{3}{4} ) {}^{2}$

$= b {}^{2} + \frac{3}{2} b + \frac{9}{16}$

2.

■ Resposta: Opção D.

$= (x - y) {}^{2} - (x + y) {}^{2}$

$= (x - y - (x + y)) \: . \: (x - y + x + y)$

$= (x - y - (x + y)) \: . \: (x + x)$

$= (x - y - x - y) \: . \: (x + x)$

$= (x - y - x - y) \: . \: 2x$

$= ( - y - y) \: . \: 2x$

$= ( - 2y) \: . \: 2x$

$= - 2y \: . \: 2x$

$= - 4xy$

3.

■ Resposta: Opção B.

$= (2a + b) {}^{2} - (a - b) {}^{2}$

$= 4a {}^{2} + 4ab + b {}^{2 } - (a {}^{2} - 2ab + b {}^{2} )$

$= 4a {}^{2} + 4ab + b {}^{2 } - a {}^{2} + 2ab - b {}^{2}$

$= 4a {}^{2} + 4ab - a {}^{2} + 2ab$

$= 3a {}^{2} + 4ab + 2ab$

$= 3a {}^{2} + 6ab$

Att. Makaveli1996