Question

(5x-1/x)to the power 2 + 8 (5x-1/x) +16

Answer 1

Let $5x-\dfrac{1}{5x} = a$

Now,

Equation : a^2 + 8a + 16

            Method 1

a^2 + 8a + 16

a^2 + ( 4 + 4 ) a + 16

a^2 + 4a + 4a + 16

a( a + 4 ) + 4( a + 4 )

( a + 4 )( a + 4 )

( a + 4 )^2

$(5x-\dfrac{1}{5x} + 4)^{2}$

         Method 2

a^2 + 8a + 16

a^2 + 2( 4a ) + 4^2

a^2 + 2ab + b^2 = ( a + b )^2

( a + 4 )^2

$(5x-\dfrac{1}{5x} + 4)^{2}$