Question

Simplify: (1/2^2+2/3y²) - (1/2x²-2/3y²)²
please give answer in explanation​

Answer 1

Answer:

Which class are you studyind friend

Answer 2

Answer:

Using Formula :-

$(a + b)² = a² + 2ab + b²$

$(a - b)² = a² - 2ab + b²$

Step-by-step explanation:

$[ \frac{1}{2} {x}^{2} + \frac{2}{3} {y}^{2} ]^{2} - [\frac{1}{2} {x}^{2} - \frac{2}{3} {y}^{2}]^{2}$

$[\scriptsize( \frac{1}{2 } {x}^{2})^{2} + \cancel2 \times \frac{1}{ \cancel2} {x}^{2} \times \frac{2}{3} {y}^{2} + ( \frac{2}{3} {y}^{2} )^{2}] - [ (\frac{1}{2} {x}^{2} )^{2} - \cancel2 \times \frac{1}{ \cancel2} {x}^{2} \times \frac{2}{3} {y}^{2} + (\frac{2}{3} {y}^{2})^{2}]$

$\scriptsize[ \frac{1}{4} {x}^{4} + \frac{2}{3} {x}^{2} {y}^{2} + \frac{4}{9} {x}^{4} ] - [ \frac{1}{4} {x}^{4} - \frac{2}{3} {x}^{2} {y}^{2} + \frac{4}{9} {y}^{4} ]$

$\scriptsize\frac{1}{4} {x}^{4} + \frac{2}{3} {x}^{2} {y}^{2} + \frac{4}{9} {x}^{4} - \frac{1}{4} {x}^{4} + \frac{2}{3} {x}^{2} {y}^{2} - \frac{4}{9} {y}^{4}$

$\scriptsize\frac{1}{4} {x}^{4} - \frac{1}{4} {x}^{4} + \frac{2}{3} {x}^{2} {y}^{2} + \frac{2}{3} {x}^{2} {y}^{2} - \frac{4}{9} {y}^{4} + \frac{4}{9} {x}^{4}$

$\frac{2 {x}^{2} {y}^{2} + 2 {x}^{2} {y}^{2} }{3}$

$\frac{4 {x}^{2} {y}^{2} }{3}$

I hope it is helpful