Hey what's the answer ? ( {y}^(2) + (5)/(7) )( {y}^(2) - (14)/(5) ) ​

Question

Hey what's the answer ?


`( {y}^(2) + (5)/(7) )( {y}^(2) - (14)/(5) )`
​

Answer 1

`\implies {\blue {\boxed {\boxed {\purple {\sf { {y}^(4) - (73 )/( 35) y² - 2}}}}}}`

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

`= ( {y}^(2) + (5)/(7) )( {y}^(2) - (14)/(5) )\\`

`= {y}^(2) ( {y}^(2) - (14)/(5) ) + (5)/(7) ( {y}^(2) - (14)/(5) )\\`

`= {y}^(2 + 2) - ( (14)/(5) ) {y}^(2) + ( (5)/(7) ) {y}^(2) - (5 * 14)/(7 * 5)\\`

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

`= {y}^(4) - \frac{14 \: {y}^(2) * 7}{5 * 7} + \frac{5 \: {y}^(2) * 5}{7 * 5} - 2\\`

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

`= {y}^(4) - (73 )/( 35) y² - 2\\`

`\boxed{ OR }`

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

where
`x=y²`,
`a=(5)/(7)` and
`b= (14)/(5)`

`= ( {y}^(2) + (5)/(7) )( {y}^(2) - (14)/(5) )\\`

`= ({ {y}^(2) })^(2) + ( (5)/(7) - (14)/(5) ) {y}^(2) - (5)/(7) * (14)/(5)\\`

`= {y}^(4) + ((5 * 5)/(7 * 5) - (14 * 7)/(5 * 7) ) {y}^(2) - 2\\`

`= {y}^(4) + ( (25 - 98)/(35) ) {y}^(2) - 2\\`

`= {y}^(4) - (73)/(35) {y}^(2) - 2\\`

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

Answer 2

Answer:
`y^4` +
`(-73)/(35)y^2`-
`2`

Explanation:

Use FOIL:

`y^4` +
`(-14)/(5)y^2` +
`(5)/(7)y^2` +
`(-70)/(35)`

Make
`(-14)/(5)y^2` and
`(5)/(7)y^2` have the same numerator:

`(-14*7)/(5*7)y^2 =(-98)/(35)y^2`

`(5*5)/(7*5) y^2=(25)/(35) y^2`

Then add like terms and simplify:

`y^4` +
`(-98)/(35)y^2` +
`(25)/(35) y^2` +
`(-70)/(35)`

`y^4` +
`(-73)/(35)y^2`-
`2`