Question

(3/4x^4 + 2/3y^3)^2 me ayudan con este por favor ​

Answer 1

Binomios al cuadrado

Vamos a usar el producto notable

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

Entonces

${( \frac{3}{4} {x}^{4} + \frac{2}{3} {y}^{3} )}^{2}$

Definimos

$a = \frac{3}{4} {x}^{4}$

$b = \frac{2}{3} {y}^{3}$

Ahora aplicamos la fórmula

${a}^{2} + 2ab + {b}^{2}$

${( \frac{3}{4} {x}^{4} )}^{2} + 2( \frac{3}{4} {x}^{4} )( \frac{2}{3} {y}^{3} ) + { ( \frac{2}{3} {y}^{3}) }^{2}$

Simplificando

$\frac{9}{16} {x}^{8} + 2( \frac{6}{12} {x}^{4} {y}^{3} ) + \frac{4}{9} {y}^{6}$

$\frac{9}{16} {x}^{8} + \frac{12}{12} {x}^{4} {y}^{3} + \frac{4}{9} {y}^{6}$

$\frac{9}{16} {x}^{8} + {x}^{4} {y}^{3} + \frac{4}{9} {y}^{6}$

Esa sería la respuesta