Question

Find the following product:  (3x² − 4xy) (3x² − 3xy)

Answer 1

Here, we will use the identity​ \[\left( x - a \right)\left( x - b \right) = x^2 - \left( a + b \right)x + ab\].

\[\left( 3 x^2 - 4xy \right)\left( 3 x^2 - 3xy \right)\]

\[ = \left( 3 x^2 \right)^2 - \left( 4xy + 3xy \right)\left( 3 x^2 \right) + 4xy \times 3xy\]

\[ = 9 x^4 - \left( 12 x^3 y + 9 x^3 y \right) + 12 x^2 y^2 \]

\[ = 9 x^4 - 21 x^3 y + 12 x^2 y^2\]