Question

Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)

Answer 1

To simplify, we will proceed as follows:

\[\left( 5x - 3 \right)\left( x + 2 \right) - \left( 2x + 5 \right)\left( 4x - 3 \right)\]

\[ = \left[ \left( 5x - 3 \right)\left( x + 2 \right) \right] - \left[ \left( 2x + 5 \right)\left( 4x - 3 \right) \right]\]

\[= \left[ 5x\left( x + 2 \right) - 3\left( x + 2 \right) \right] - \left[ 2x\left( 4x - 3 \right) + 5\left( 4x - 3 \right) \right]\]            (Distributive law)

\[= 5 x^2 + 10x - 3x - 6 - 8 x^2 + 6x - 20x + 15\]

\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\]          (Rearranging)

\[= 5 x^2 - 8 x^2 + 10x - 3x + 6x - 20x - 6 + 15\]

\[ = - 3 x^2 - 7x + 9\]       (Combining like terms)

Hence, the answer is   \[- 3 x^2 - 7x + 9\].