Quadrado da diferença multiplicado pela soma de dois números
Agora vamos multiplicar o quadrado das diferenças, pelas somas dos dois números, conforme a regra vista.
a)$\underbrace{(3x – 2y)^2}\cdot{\overbrace{(3x + 2y)}} $
b)$\underbrace{(5a – bx)^2}\cdot{\overbrace{(5a + bx)}}$
c)$\underbrace{(1 – 5x)^2}\cdot{\overbrace{(1 + 5x)}}$
d)$\underbrace {(6t – 4s)^2}\cdot{\overbrace{(6t+ 4s)}}$
e)$\underbrace{(8i – z)^2}\cdot{\overbrace{(8i +z)}}$
f)$\underbrace{(4n – 5m)^2}\cdot{\overbrace{(4n +5m)}}$
g)$\underbrace{(r – pq)^2}\cdot{\overbrace{(r + pq)}} $
Vamos resolver aplicando a regra.
a)$\underbrace{(3x – 2y)^2}\cdot{\overbrace{(3x + 2y)}} $
$\underbrace{{(3x)}^3} -\overbrace {{(3x)}^2\cdot{(2y)}} – \underbrace{3x\cdot {(2y)^2}} + \overbrace{{(2y)}^3}$
$ 27x^3 – 18x^2y – 12xy^2 + 8y^3 $
b)$\underbrace{(5a – bx)^2}\cdot{\overbrace{(5a + bx)}}$
$\underbrace{{(5a)}^3} -\overbrace{{(5a)^2}\cdot{(bx)}} – \underbrace{5a\cdot{(bx)}^2} +\overbrace{{(bx)}^3}$
$ 125 a^3 – 25abx – 5ab^2x^2 + b^3x^3 $
c)$\underbrace{(1 – 5x)^2}\cdot{\overbrace{(1 + 5x)}}$
$\underbrace{1^3} -\overbrace{ 1^2\cdot 5x} -\underbrace{1\cdot {(5x)^2}} +{{(5x)}^3}$
$ 1 – 5x – 25x^2 + 125x^3 $
d)$\underbrace {(6t – 4s)^2}\cdot{\overbrace{(6t+ 4s)}}$
$\underbrace{{(6t)}^3} -\overbrace {{(6t)}^2\cdot {(4s)}} – \underbrace{6t\cdot {(4s)}^2} +\overbrace {{(4s)}^3}$
$ 216t^3 – 144t^2s – 96ts^2 + 64s^3 $
e)$\underbrace{(8i – z)^2}\cdot{\overbrace{(8i +z)}}$
$\underbrace{{(8i)}^3} -\overbrace {{(8i)^2}\cdot {(z)}} – \underbrace{8i\cdot z^2} +\overbrace{ z^3}$
$ 512i^3 – 64i^2z – 8iz^2 + z^3$
f)$\underbrace{(4n – 5m)^2}\cdot{\overbrace{(4n +5m)}}$ $\underbrace{{(4n)}^3} -\overbrace {{(4n)^2}\cdot{(5m}} -\underbrace{4n\cdot {((5m)}^2} +\overbrace {{(5m)}^3}$
$ 64n^3 – 80mn^2 – 100m^2n + 125m^3 $
g)$\underbrace{(r – pq)^2}\cdot{\overbrace{(r + pq)}}$
$\underbrace{ r^3} -\overbrace{ r^2\cdot {(pq)}} -\underbrace{r\cdot {(pq)}^2} +\overbrace{ {(pq)}^3}$
$ r^3 – pqr^2 – p^2q^2r + p^3q^3 $
Vamos deixar uns exemplos para seu treinamento. Não esqueça que em caso de dúvidas pode fazer contato e pedir esclarecimento.
h)$\underbrace{(9 – 3x)^2}\cdot{\overbrace{(9 + 3x)}}$
i) $\underbrace{(4m -n)^2}\cdot{\underbrace{(4m + n)}}$
j)$\underbrace{(5a – 2b)^2}\cdot{\overbrace{(5a – 2b)}}$
l)$\underbrace{(7u – 3v)^2}\cdot{\overbrace{(7u + 3v)}}$
m)$\underbrace{(2mn – 7)^2}\cdot{\overbrace{(2mn + 7)}}$
n)$\underbrace{(5pr – 4tu)^2}\cdot{\overbrace{(5pr + 4tu)}}$
o)$\underbrace{(7f – 3g)^2}\cdot{\overbrace{(7f + 3g)}}$
p)$\underbrace{(9 – 6n)^2}\cdot{\overbrace{(9 + 6n)}}$
Curitiba, 26 de junho de 2018
Décio Adams
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