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Addition and Subtraction of Algebraic Expressions

Simplify:x3-2...

Question

Simplify:
(x³ − 2x² + 5x − 7)(2x − 3)

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Solution

To simplify, we will proceed as follows:

$(x^{3} - 2 x^{2} + 5 x - 7) (2 x - 3) = 2 x (x^{3} - 2 x^{2} + 5 x - 7) - 3 (x^{3} - 2 x^{2} + 5 x - 7) = 2 x^{4} - 4 x^{3} + 10 x^{2} - 14 x - 3 x^{3} + 6 x^{2} - 15 x + 21$
$= 2 x^{4} - 4 x^{3} - 3 x^{3} + 10 x^{2} + 6 x^{2} - 14 x - 15 x + 21$ (Rearranging)
$= 2 x^{4} - 7 x^{3} + 16 x^{2} - 29 x + 21$ (Combining like terms)

Thus, the answer is $2 x^{4} - 7 x^{3} + 16 x^{2} - 29 x + 21$ .

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