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प्रश्न
Simplify:
(x2 − 3x + 2)(5x − 2) − (3x2 + 4x − 5)(2x − 1)
उत्तर
To simplify, we will proceed as follows:
\[\left( x^2 - 3x + 2 \right)\left( 5x - 2 \right) - \left( 3 x^2 + 4x - 5 \right)\left( 2x - 1 \right)\]
\[ = \left[ \left( x^2 - 3x + 2 \right)\left( 5x - 2 \right) \right] - \left[ \left( 3 x^2 + 4x - 5 \right)\left( 2x - 1 \right) \right]\]
\[= \left[ 5x\left( x^2 - 3x + 2 \right) - 2\left( x^2 - 3x + 2 \right) \right] - \left[ 2x\left( 3 x^2 + 4x - 5 \right) - 1 \times \left( 3 x^2 + 4x - 5 \right) \right]\] (Distributive law)
\[= \left[ 5 x^3 - 15 x^2 + 10x - \left( 2 x^2 - 6x + 4 \right) \right] - \left[ 6 x^3 + 8 x^2 - 10x - 3 x^2 - 4x + 5 \right]\]
\[ = \left[ 5 x^3 - 15 x^2 + 10x - 2 x^2 + 6x - 4 \right] - \left[ 6 x^3 + 8 x^2 - 10x - 3 x^2 - 4x + 5 \right]\]
\[ = 5 x^3 - 15 x^2 + 10x - 2 x^2 + 6x - 4 - 6 x^3 - 8 x^2 + 10x + 3 x^2 + 4x - 5\]
\[= 5 x^3 - 6 x^3 - 15 x^2 - 2 x^2 - 8 x^2 + 3 x^2 + 10x + 6x + 10x + 4x - 5 - 4\] (Rearranging)
\[= - x^3 - 22 x^2 + 30x - 9\] (Combining like terms)
Thus, the answer is \[- x^3 - 22 x^2 + 30x - 9\].
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