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Question
Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)
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Solution
To simplify, we will proceed as follows:
\[\left( 2 x^2 + 3x - 5 \right)\left( 3 x^2 - 5x + 4 \right)\]
\[= 2 x^2 \left( 3 x^2 - 5x + 4 \right) + 3x\left( 3 x^2 - 5x + 4 \right) - 5\left( 3 x^2 - 5x + 4 \right)\] (Distributive law)
\[= 6 x^4 - 10 x^3 + 8 x^2 + 9 x^3 - 15 x^2 + 12x - 15 x^2 + 25x - 20\]
\[= 6 x^4 - 10 x^3 + 9 x^3 + 8 x^2 - 15 x^2 - 15 x^2 + 12x + 25x - 20\] (Rearranging)
\[= 6 x^4 - x^3 - 22 x^2 + 36x - 20\] (Combining like terms)
Thus, the answer is \[6 x^4 - x^3 - 22 x^2 + 36x - 20\].
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