Question

slove using identities (x^2+5)(x^2-10)

Answer 1

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Let x² = y

( x² + 5 )( x² - 10 )
( y + 5 )[ y + ( - 10 ) ]

Now, this quation is similar to ( x + a )( x + b ) =
x² + ( a + b )x + ab

= y² + [ 5 + ( - 10 ) ]y + ( 5 )( - 10 )
= y² - 5y - 50

We get, ( x² )² - 5( x² ) - 50
x⁴ - 5x² - 50

Verification

= y² - 5y - 50

Split the middle term

y² - 10y + 5y - 50
y ( y - 10 ) + 5 ( y - 10 )
( y + 5 )( y - 10 )

Now, replace y with x²

( x² + 5 )( x² - 10 )

Hope it helps