Question

Write the following square of binomial as trinomial: (a²b − bc²)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.

\[\left( a^2 b - b c^2 \right)^2 \]

\[ = \left( a^2 b \right)^2 - 2\left( a^2 b \right)\left( b c^2 \right) + \left( b c^2 \right)^2 \]

\[ = a^4 b^2 - 2 a^2 b^2 c^2 + b^2 c^4\]