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Ainat [17]
3 years ago
8

Hey what's the answer ?

8%20%7By%7D%5E%7B2%7D%20%20-%20%20%5Cfrac%7B14%7D%7B5%7D%20%29" id="TexFormula1" title="( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )" alt="( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
3241004551 [841]3 years ago
7 0

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

MissTica3 years ago
5 0

\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\\

<h3>\boxed{ OR   }</h3>

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}}}}}

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