Question

Calcule os produtos notáveis:
a) (xy3 + 3)²=
b) (5 + x2 )2 =
c) (7 - 3x)²=
d) (2x - 4)²=
e) (3xy5 + 2)²=
f) (2a – x2 )²=
g) (7y - 3x)²=
h) (2x² - y).(2x² + y)=
i) (x² - 3y).(x² + 3y)=
j) (xy3 + 3z).(xy3 - 3z)=

Answer 1

Explicação passo-a-passo:

a)

(xy³ + 3)² = (xy³)² + 2.xy³.3 + 3²

(xy³ + 3)² = x²y⁶ + 6xy³ + 9

b)

(5 + x²)² = 5² + 2.5.x² + (x²)²

(5 + x²)² = 25 + 10x² + x⁴

c)

(7 - 3x)² = 7² - 2.7.3x + (3x)²

(7 - 3x)² = 49 - 42x + 9x²

d)

(2x - 4)² = (2x)² - 2.2x.4 + 4²

(2x - 4)² = 4x² - 16x + 16

e)

(3xy⁵ + 2)² = (3xy⁵)² + 2.3xy⁵.2 + 2²

(3xy⁵ + 2)² = 9x²y¹⁰ + 12xy⁵ + 4

f)

(2a - x²)² = (2a)² - 2.2a.x² + (x²)²

(2a - x²)² = 4a² - 4ax² + x⁴

g)

(7y - 3x)² = (7y)² - 2.7y.3x + (3x)²

(7y - 3x)² = 49y² - 42xy + 9x²

h)

(2x² - y).(2x² + y) = (2x²)² - y²

(2x² - y).(2x² + y) = 4x⁴ - y²

i)

(x² - 3y).(x² + 3y) = (x²)² - (3y)²

(x² - 3y).(x² + 3y) = x⁴ - 9y²

j)

(xy³ + 3z).(xy³ - 3z) = (xy³)² - (3z)²

(xy³ + 3z).(xy³ - 3z) = x²y⁶ - 9z²

Answer 2

Oie, Td Bom?!

a)

$= (xy {}^{3} + 3) {}^{2}$

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

$= x {}^{2} y {}^{6} + 6xy {}^{3} + 9$

b)

$= (5 + x {}^{2} ) {}^{2}$

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

$= 25 + 10x {}^{2} + x {}^{4}$

$= x {}^{4} + 10x {}^{2} + 25$

c)

$= (7 - 3x) {}^{2}$

$= 7 {}^{2} - 2 \: . \: 7 \: . \: 3x + (3x) {}^{2}$

$= 49 - 42x + 9x {}^{2}$

$= 9x {}^{2} - 42x + 49$

d)

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

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

$= 4x {}^{2} - 16x + 16$

e)

$= (3xy {}^{5} + 2) {}^{2}$

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

$= 9x {}^{2} y {}^{10} + 12x y{}^{5} + 4$

f)

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

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

$= 4a {}^{2} - 4ax {}^{2} + x {}^{4}$

g)

$= (7y - 3x) {}^{2}$

$= (7y) {}^{2} - 2 \: . \: 7y \: . \: 3x + (3x) {}^{2}$

$= 49y {}^{2} - 42xy + 9x {}^{2}$

h)

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

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

$= 4x {}^{4} - y {}^{2}$

i)

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

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

$= x {}^{4} - 9y {}^{2}$

j)

$= (xy {}^{3} + 3z) \: . \: (xy {}^{3} - 3z)$

$= (xy {}^{3} ) {}^{2} - (3z) {}^{2}$

$= x {}^{2} y {}^{6} - 9z {}^{2}$

Att. Makaveli1996