Question

How do you factor `49p^2+28ps+4s^2`?

Answer 1

`49p^2+28ps+4s^2=(7p+2s)^2`

Explanation:

The equation `49p^2+28ps+4s^2` is in fact a quadratic equation. Observe that it has two variables and each monomial has a degree of `2`. Such a polynomial is called homogeneous.

If we divide each term of the polynomial by `s^2`, we get `49p^2/s^2+28(ps)/s^2+4` or `49(p/s)^2+28p/s+4` and putting `p/s=x`, we get

`49x^2+28x+4`.

Now we can factorize it like any quadratic equation by either completing square method or splitting the middle term.

What is typical about this is that in fact polynomial is a complete square.

As `49p^2+28ps+4s^2`

= `(7p)^2+2xx7pxx2s+(2s)^2`

= `(7p+2s)^2`

hence the factors.