Cubo da diferença

Vamos fazer o mesmo com a regra do cubo da diferença. a)$\underbrace{{(4m – 2)}^3}$

b)$\underbrace{{(3x – 5y)}^3}$

c)$\underbrace{{(9 – 5a)}^3}$

d)$\underbrace{{(5 – 4x)}^3}$

e)$\underbrace{{(10 – 5c)}^3}$

f)$\underbrace{{(3ab – x)}^3}$

g)$\underbrace{(pq^{2} – rq)^3}$

a)$\underbrace{{(4m – 2)}^3}$

$\underbrace { {(4m)}^{3}} -\overbrace{ 3\cdot {(4m)^{2}}\cdot 2} +\underbrace{ 3\cdot{(4m)}\cdot 2^{2}} -\overbrace{ 2^{3}}$

$  64m^{3} – 96m^{2} + 48m – 8 $

b)$\underbrace{{(3x – 5y)}^3}$

$\underbrace{ (3x)^{3}} -\overbrace{ 3\cdot (3x)^{2}\cdot {(5y)}} +\underbrace{ 3\cdot{(3x)}\cdot (5y)^{2}} -\overbrace{{(5y)}^{3}}$

$ 27x^3 – 135x^{2}y + 225xy^{2} – 125y^{3} $

c)$\underbrace{{(9 – 5a)}^3}$

$\underbrace{(9)^{3}} -\overbrace{ 3\cdot (9)^2\cdot (5a)} +\underbrace{ 3\cdot 9 \cdot(5a)^{2}} -\overbrace{(5a)^{3}}$

$ 729 – 1215 a + 675 a^2 – 125 a^3 $

d)$\underbrace{{(5 – 4x)}^3}$

$\underbrace{  5^{3}} -\overbrace{ 3\cdot 5^{2}\cdot (4x)} +\underbrace{ 3\cdot 5\cdot (4x)^{2}} – \overbrace{{(4x)}^{3}}$

$  125 – 300x + 120 x^{2} – 64x^{3} $

e)$\underbrace{{(10 – 5c)}^3}$

$\underbrace{ 10^{3}} -\overbrace{ 3\cdot(5)^{2}\cdot (5c)} +\underbrace{ 3\cdot{10}\cdot {(5c)}^{2}} -\overbrace{ {(5c)}^{3}}$

$ 1000 – 375 c + 750 c^{2} – 125c^{3} $

f)$\underbrace{{(3ab – x)}^3}$

$\underbrace{{(3ab)}^{3}} -\overbrace{ 3\cdot {(3ab)}^{2}\cdot x} +\underbrace{ 3\cdot{(3ab)}\cdot x^{2}} -\overbrace{ x^{3}}$

$  27a^{3}b^{3} – 27a^{2}b^{2}x + 9 abx^{2} – x^{3} $

g)$\underbrace{{(pq^{2} – rq)}^3}$

$\underbrace{ {(pq^{2})}^{3}} -\overbrace{ 3\cdot {(pq^{2})}^{2}\cdot rq} +\underbrace{ 3\cdot {(pq^{2})}\cdot {(rq)}^{2}} -\overbrace{ {(rq)}^{3}}$

$   p^{3}q^{6} – 3p^{2}q^{5}r + 3pq^{4}r^{2} – q^{3}r^{3} $

Exercícios para você leitor treinar sua habilidade. Em caso de dúvida, não perca tempo. Faça contato e exponha sua dificuldade. Estou à disposição para ajudar.

h)$\underbrace{(7x – 5yz)^3}=?$

i)$\underbrace{(mn – r)^3}=?$

j)$\underbrace{(3a – 2bc)^4}=?$

l)$\underbrace{(u – vx)^3}=?$

m)$\underbrace{(6f – 2h)^3}=?$

n)$\underbrace{(5z – 3y)^3}=?$

o)$\underbrace{(4x – 7y)^3}=?$

Curitiba, 26 de junho de 2018

Décio Adams

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