Question

$\frac{4}{25} x6-\frac{3}{10} x3y3+\frac{9}{64}y6$

Answer 1

Respuesta:

4/25x^6 - 3/10x^3y^3 + 9/64y^6

=4 / (6*5*x) - 3 / (3*3*10*x*y) + 9(6*64*y)

= -1 / (3*x*y) + 2 / (15*y) + 3 / (128*y)

Answer 2

Respuesta:

$(\frac{2}{5}x^{3}-\frac{3}{8}y^{3})^{2}$

Explicación paso a paso:

$\frac{4}{25}x^6-\frac{3}{10}x^3y^3+\frac{9}{64}y^6$

$(\frac{2}{5}x^{3})^{2}-\frac{4(3)}{4(10)}x^3y^3+(\frac{3}{8}y^{3})^{2}\\\\(\frac{2}{5}x^{3})^{2}-\frac{2(2)(3)}{4(5)(2)}x^3y^3+(\frac{3}{8}y^{3})^{2}  \\ \\(\frac{2}{5}x^{3})^{2}-\frac{2(2)(3)}{(5)(4.2)}x^3y^3+(\frac{3}{8}y^{3})^{2}   \\\\(\frac{2}{5}x^{3})^{2}-\frac{2(2)(3)}{(5)(8)}x^3y^3+(\frac{3}{8}y^{3})^{2}  \\\\(\frac{2}{5}x^{3})^{2}-2(\frac{2}{5})(\frac{3}{8})x^3y^3+(\frac{3}{8}y^{3})^{2}$

$(\frac{2}{5}x^{3})^{2}-2(\frac{2}{5}x^3)(\frac{3}{8}y^3)+(\frac{3}{8}y^{3})^{2}$

RECORDEMOS: "Trinomio cuadrado perfecto"

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

tenemos

$(\frac{2}{5}x^{3})^{2}-2(\frac{2}{5}x^3)(\frac{3}{8}y^3)+(\frac{3}{8}y^{3})^{2}$

Entonces:   a=$\frac{2}{5}x^{3}$      y    b=$\frac{3}{8}y^{3}$

Reemplazar a y  b    en     $(a-b)^{2}$

$(\frac{2}{5}x^{3}-\frac{3}{8}y^{3})^{2}$

y eso es la respuesta.