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Conversion of Statements to Linear Equations

Simplify:2 x2...

Question

Simplify:
(2x² + 3x − 5)(3x² − 5x + 4)

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Solution

To simplify, we will proceed as follows:

$(2 x^{2} + 3 x - 5) (3 x^{2} - 5 x + 4)$
$= 2 x^{2} (3 x^{2} - 5 x + 4) + 3 x (3 x^{2} - 5 x + 4) - 5 (3 x^{2} - 5 x + 4)$ (Distributive law)
$= 6 x^{4} - 10 x^{3} + 8 x^{2} + 9 x^{3} - 15 x^{2} + 12 x - 15 x^{2} + 25 x - 20$
$= 6 x^{4} - 10 x^{3} + 9 x^{3} + 8 x^{2} - 15 x^{2} - 15 x^{2} + 12 x + 25 x - 20$ (Rearranging)
$= 6 x^{4} - x^{3} - 22 x^{2} + 36 x - 20$ (Combining like terms)

Thus, the answer is $6 x^{4} - x^{3} - 22 x^{2} + 36 x - 20$ .

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