Question

Write the following square of binomial as trinomial: 

\[\left( x + \frac{x^2}{2} \right)^2\]

Answer 1

 We will use the identities

\[\left( a + b \right)^2 = a^2 + 2ab + b^2 \text { and } \left( a - b \right)^2 = a^2 - 2ab + b^2\] to convert the squares of binomials as trinomials.

\[ \left( x + \frac{x^2}{2} \right)^2 \]

\[ = x^2 + 2x\left( \frac{x^2}{2} \right) + \left( \frac{x^2}{2} \right)^2 \]

\[ = x^2 + x^3 + \frac{x^4}{4}\]