Question

Hey what's the answer ?
$( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )$
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Answer 1

Answer: $y^4$ + $\frac{-73}{35}y^2$- $2$

Step-by-step explanation:

Use FOIL:

$y^4$ + $\frac{-14}{5}y^2$ + $\frac{5}{7}y^2$ + $\frac{-70}{35}$

Make  $\frac{-14}{5}y^2$ and $\frac{5}{7}y^2$ have the same numerator:

$\frac{-14*7}{5*7}y^2 =\frac{-98}{35}y^2$

$\frac{5*5}{7*5} y^2=\frac{25}{35} y^2$

Then add like terms and simplify:

$y^4$ + $\frac{-98}{35}y^2$ + $\frac{25}{35} y^2$ + $\frac{-70}{35}$

$y^4$ + $\frac{-73}{35}y^2$- $2$

Answer 2

$\implies {\blue {\boxed {\boxed {\purple {\sf { {y}^{4} - \frac{73 }{ 35} y² - 2}}}}}}$

$\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}$

$= ( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )$

$= {y}^{2} ( {y}^{2} - \frac{14}{5} ) + \frac{5}{7} ( {y}^{2} - \frac{14}{5} )$

$= {y}^{2 + 2} - ( \frac{14}{5} ) {y}^{2} + ( \frac{5}{7} ) {y}^{2} - \frac{5 \times 14}{7 \times 5}$

$= {y}^{4} - \frac{14 \: {y}^{2} }{5} + \frac{5 \: {y}^{2} }{7} - 2$

$= {y}^{4} - \frac{14 \: {y}^{2} \times 7}{5 \times 7} + \frac{5 \: {y}^{2} \times 5}{7 \times 5} - 2$

$= {y}^{4} - \frac{ 98 \: {y}^{2} + 25 \: {y}^{2} }{35} - 2$

$= {y}^{4} - \frac{73 }{ 35} y² - 2$

$\boxed{ OR }$

By using the identity $(x + a)(x - b) = {x}^{2} + (a - b)x - ab$,

where $x=y²$, $a=\frac{5}{7}$ and $b= \frac{14}{5}$

$= ( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )$

$= ({ {y}^{2} })^{2} + ( \frac{5}{7} - \frac{14}{5} ) {y}^{2} - \frac{5}{7} \times \frac{14}{5}$

$= {y}^{4} + (\frac{5 \times 5}{7 \times 5} - \frac{14 \times 7}{5 \times 7} ) {y}^{2} - 2$

$= {y}^{4} + ( \frac{25 - 98}{35} ) {y}^{2} - 2$

$= {y}^{4} - \frac{73}{35} {y}^{2} - 2$

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}$