Question

Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)

Answer 1

To simplify, we will proceed as follows:

\[\left( 3x - 2 \right)\left( 2x - 3 \right) + \left( 5x - 3 \right)\left( x + 1 \right)\]

\[ = \left[ \left( 3x - 2 \right)\left( 2x - 3 \right) \right] + \left[ \left( 5x - 3 \right)\left( x + 1 \right) \right]\]

\[= \left[ 3x\left( 2x - 3 \right) - 2\left( 2x - 3 \right) \right] + \left[ 5x\left( x + 1 \right) - 3\left( x + 1 \right) \right]\]            (Distributive law)

\[= 6 x^2 - 9x - 4x + 6 + 5 x^2 + 5x - 3x - 3\]

\[= 6 x^2 + 5 x^2 - 9x - 4x + 5x - 3x - 3 + 6\]          (Rearranging)

\[= 11 x^2 - 11x + 3\]                (Combining like terms)

Thus, the answer is \[11 x^2 - 11x + 3\].