Question

ayudenme a resolver este ejercicio

Answer 1

Hola!

Explicación paso a paso:

a)

${( \frac{4}{5} {a}^{3} {b}^{2}x + \frac{3}{4} ab {x}^{2} ) }^{2} \\ = {(\frac{4}{5} {a}^{3} {b}^{2}x)}^{2} + 2(\frac{4}{5} {a}^{3} {b}^{2}x) ( \frac{3}{4} ab {x}^{2} ) + {(\frac{3}{4} ab {x}^{2} )}^{2} \\ = \frac{16}{25} {a}^{6} {b}^{4} {x}^{2} + \frac{24}{20} {a}^{4} {b}^{3} + {x}^{3} + \frac{9}{16} {a}^{2} {b}^{2} {x}^{4}$

b)

$(x + \frac{1}{2} ).(x + 5) \\ = {x}^{2} + 5x + \frac{x}{2} + \frac{5}{2} \\ = {x}^{2} + \frac{11x}{2} + \frac{5}{2}$

c)

$( \frac{2}{3} x {y}^{2} - 3).( \frac{2}{3} x {y}^{2} + 3) \\ = {(\frac{2}{3} x {y}^{2})}^{2} - {3}^{2} \\ = \frac{4}{9} {x}^{2} {y}^{4} - 9$

d)

${(1.2 \: {x}^{3} - 0.5x)}^{2} \\ = {( \frac{6}{5} {x}^{3} - \frac{1}{2}x )}^{2} \\ = {(\frac{6}{5} {x}^{3} )}^{2} - 2(\frac{6}{5} {x}^{3} )(\frac{1}{2}x) + {(\frac{1}{2}x)}^{2} \\ = \frac{36}{25} {x}^{6} - \frac{6}{5} {x}^{4} + \frac{1}{4} {x}^{2} \\ = 1.44 \: {x}^{6} - 1.2 \: {x}^{4} + 0.25 \: {x}^{2}$

e)

${( \frac{2}{3} {x}^{3} + \frac{1}{2} )}^{2} \\ = {(\frac{2}{3} {x}^{3} )}^{2} + 2(\frac{2}{3} {x}^{3} )( \frac{1}{2} ) + {( \frac{1}{2}) }^{2} \\ = \frac{4}{9} {x}^{6} + \frac{2}{3} {x}^{3} + \frac{1}{4}$