Question

Resolva:
( 5 a + 2 b )³ =

( x² - 4 y )³ =

( 3 x + 5) . ( 3 x – 5 ) =

Desenvolva as seguintes expressões:
( 3x + y )³ =

( 4x – 1 )³ =


Fatore os seguintes polinômios:
10 x + 10 y =

a ² x + a b x =


a ² + a b + a x + b x =

a . ( x + y ) + b . ( x + y ) =
​

Answer 1

Δ Olá Δ

Resolva:

( 5 a + 2 b )³ =

(5a)³ + 3(5a)² . 2b + 3 . 5a(2b)² + (2b)³

125a³ + 150 a²b + 60ab² +8b³

( x² - 4 y )³ =

(x²)³ - 3(x²)² . 4y + 3x² (4y)² - (4y)³

x⁶ - 12x⁴y +48x²y² - 64y³

( 3 x + 5) . ( 3 x – 5 ) =

(3x)² - 5²

9x² - 25

Desenvolva as seguintes expressões:

( 3x + y )³ =

( 4x – 1 )³ =

Fatore os seguintes polinômios:

10 x + 10 y =

10 (x + y)

a ² x + a b x =

aax + abx

xa (a + b)

a ² + a b + a x + b x =

a(a + b) + x(a + b)

(a + b)(a + x)

a . ( x + y ) + b . ( x + y ) =

​

(x + y)(a + b)

Δ Espero ter ajudado Δ

Answer 2

Oie, Td Bom?!

1.

a)

$= (5a + 2b) {}^{3}$

$= (5a) {}^{3} + 3 \: . \: (5a) {}^{2} \: . \: 2b + 3 \: . \: 5a \: . \: (2b) {}^{2} + (2b) {}^{3}$

$= 125a {}^{3} + 3 \: . \: 25a {}^{2} \: . \: 2b + 3 \: . \: 5a \: . \: 4b {}^{2} + 8b {}^{3}$

$= 125a {}^{3} + 150a {}^{2} b + 60ab {}^{2} + 8b {}^{3}$

b)

$= (x {}^{2} - 4y) {}^{3}$

$= (x {}^{2} ) {}^{3} - 3 \: . \: (x {}^{2} ) {}^{2} \: . \: 4y + 3x {}^{2} \: . \: (4y) {}^{2} - (4y) {}^{3}$

$= x {}^{6} - 3x {}^{4} \: . \: 4y + 3x {}^{2} \: . \: 16y {}^{2} - 64y {}^{3}$

$= x{}^{6} - 12x {}^{4} y + 48x {}^{2} y {}^{2} - 64y {}^{3}$

c)

$= (3x + 5) \: . \: (3x - 5)$

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

$= 9x {}^{2} - 25$

2.

a)

$= (3x + y) {}^{3}$

$= (3x) {}^{3} + 3 \: . \: (3x) {}^{2} \: . \: y + 3 \: . \: 3xy {}^{2} + y {}^{3}$

$= 27x {}^{3} + 3 \: . \: 9x {}^{2} y + 9xy {}^{2} + y {}^{3}$

$= 27x {}^{3} + 27x {}^{2} y + 9xy {}^{2} + y {}^{3}$

b)

$= (4x - 1) {}^{3}$

$= (4x) {}^{3} - 3 \: . \: (4x) {}^{2} \: . \: 1 + 3 \: . \: 4x \: . \: 1 {}^{2} - 1 {}^{3}$

$= 64x {}^{3} - 3 \: . \: 16x {}^{2} \: . \: 1 + 3 \: . \: 4x \: . \: 1 - 1$

$= 64x {}^{3} - 48x {}^{2} + 12x - 1$

3.

a)

$= 10x + 10y$

$= 10(x + y)$

b)

$= a {}^{2} x + abx$

$= ax \: . \: (a + b)$

c)

$= a {}^{2} + ab + ax + bx$

$= a \: . \: (a + b) + x \: . \: (a + b)$

$= (a + b) \: . \: (a + x)$

d)

$= a \: . \: (x + y) + b \: . \: (x + y)$

$= (x + y) \: . \: (a + b)$

Att. Makaveli1996