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Question
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
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Solution
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 \[- 3 x^2 - 7x + 9\].
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