Question

expand the given identity 1 by 4 a minus 1 by 2 b + 1 whole to the power 2​

Answer 1

Answer:

( (1/4)a - (1/2)b + 1 )² = a²/16 + b²/4 + 1 +  ab/4 + b + a/2)  

Step-by-step explanation:

Since we have to expend

( (1/4)a - (1/2)b + 1 )²

we know that

(a + b + c) = a² + b² + c² + 2( ab + bc + ca)

In our case we need to do following replacement

a ⇔ a/4 , b ⇔ b/2 and c ⇔ 1

So after properly replacement we get

( (1/4)a - (1/2)b + 1 )² = (a/4)² + (b/2)² + 1² + 2( (a/4)(b/2) + (b/2)(1) + 1(a/4) )

                                = a²/16 + b²/4 + 1 +  ab/4 + b + a/2  

Hence

( (1/4)a - (1/2)b + 1 )² = a²/16 + b²/4 + 1 +  ab/4 + b + a/2)