Question

Por favor me pueden explicar como se hacen estos ejercicios

Answer 1

Hola!

Explicación paso a paso:

■》Formula:

$formula \: del \: binomio \: al \: cuadrado : \\ {(a + b)}^{2} = {(a)}^{2} + 2(a)(b) + {(b)}^{2}$

■》Solución:

a)

${(x + 5)}^{2} \\ = {(x)}^{2} +2(x)(5) + {(5)}^{2} \\ = {x}^{2} + 10x + 25$

b)

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

c)

${(4x + 3 {y}^{3} )}^{2} \\ = {(4x)}^{2} + 2(4x)(3 {y}^{3} ) + {(3 {y}^{3} )}^{2} \\ = 16 {x}^{2} + 24x {y}^{3} + 9 {y}^{6}$

d)

${(z {a}^{2} + \frac{5}{2} z)}^{2} \\ \\ = {(z {a}^{2}) }^{2} + 2(z {a}^{2})( \frac{5}{2} z) + {( \frac{5}{2}z) }^{2} \\ \\ = {z}^{2} {a}^{4} + 5 {z}^{2} {a}^{2} + \frac{25 {z}^{2} }{4}$

e)

${(5 {a}^{5} + \frac{1}{3} {a}^{2} )}^{2} \\ \\ = {(5 {a}^{5} )}^{2} + 2(5 {a}^{5} )( \frac{1}{3} {a}^{2} ) + {( \frac{1}{3} {a}^{2} ) }^{2} \\ \\ = 25 {a}^{10} + \frac{10 {a}^{7} }{3} + \frac{ {a}^{4} }{9}$

f)

${( - 4 {y}^{2} + \frac{2}{5} {y}^{3} ) }^{2} \\ \\ = {( - 4 {y}^{2}) }^{2} + 2( - 4 {y}^{2} )( \frac{2}{5} {y}^{3} ) + {( \frac{2}{5} {y}^{3}) }^{2} \\ \\ = 16 {y}^{4} - \frac{ 16 {y}^{5} }{5} + \frac{4 {y}^{6} }{25}$