Question

ayuda!!!!!!!!!!!!!!!!!!!!!!!
obtén los productos notables

Answer 1

Explicación paso a paso:

Hola.

En los 2 primero podemos aplicar DIFERENCIA DE CUADRADOS

${x}^{2} - {y}^{2} = (x + y)(x - y )\\ (x + y)(x - y) = {x}^{2} - {y}^{2}$

1)

$(0.1 {x}^{2} + 0.2 {y}^{3} )(0.1 {x}^{2} - {y}^{3} ) \\ = {(0.1 {x}^{2}) }^{2} - {(0.2 {y}^{3}) }^{2} \\ = {( \frac{1}{10} {x}^{2}) }^{2} - {( \frac{2}{10} {y}^{3}) }^{2} \\ = \frac{1}{100} {x}^{4} - \frac{4}{100} {y}^{6} \\ = 0.01 {x}^{4} - 0.04 {y}^{6}$

2)

$(2x - 6)(2x + 6) \\ = {(2x)}^{2} - {(6})^{2} \\ = 4 {x}^{2} - 36$

En la última imagen aplicaremos BINOMIO AL CUADRADO

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

Resolveré el último

${(6 {x}^{2} - 1)}^{2} \\ = {(6 {x}^{2} )}^{2} + {1}^{2} - 2(6 {x}^{2} )(1) \\ = 36 {x}^{4} + 1 - 12 {x}^{2} \\ = 36 {x}^{4} - 12 {x}^{2} + 1$