Question

Factorize x^2/16+xy+4y^2​

Answer 1

`(x^2)/(16) +xy+4y^2` can be factored out as:
`((x)/(4) +2\,y)^2`

Explanation:

Recall the formula for the perfect square of a binomial :

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

Now, let's try to identify the values of
`a` and
`b` in the given trinomial.

Notice that the first term and the last term are perfect squares:

`(x^2)/(16) = ((x)/(4) )^2\\4y^2=(2y)^2`

so, we can investigate what the middle term would be considering our
`a=(x)/(4)`, and
`b=2y`:

`2\,a\,b=2\,((x)/(4)) \,(2\,y)=x\,y`

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

`((x)/(4) +2\,y)^2`