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Question
Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
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Solution
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 \[11 x^2 - 11x + 3\].
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