Simplify:
(x³ − 2x² + 3x − 4) (x −1) − (2x − 3)(x² − x + 1)

Open in App

Solution

To simplify,we will proceed as follows:

$(x^{3} - 2 x^{2} + 3 x - 4) (x - 1) - (2 x - 3) (x^{2} - x + 1) = [(x^{3} - 2 x^{2} + 3 x - 4) (x - 1)] - [(2 x - 3) (x^{2} - x + 1)]$
$= [x (x^{3} - 2 x^{2} + 3 x - 4) - 1 (x^{3} - 2 x^{2} + 3 x - 4)] - [2 x (x^{2} - x + 1) - 3 (x^{2} - x + 1)]$ (Distributive law)
$= [x (x^{3} - 2 x^{2} + 3 x - 4) - 1 (x^{3} - 2 x^{2} + 3 x - 4)] - [2 x (x^{2} - x + 1) - 3 (x^{2} - x + 1)] = x^{4} - 2 x^{3} + 3 x^{2} - 4 x - x^{3} + 2 x^{2} - 3 x + 4 - [2 x^{3} - 2 x^{2} + 2 x - 3 x^{2} + 3 x - 3] = x^{4} - 2 x^{3} + 3 x^{2} - 4 x - x^{3} + 2 x^{2} - 3 x + 4 - 2 x^{3} + 2 x^{2} - 2 x + 3 x^{2} - 3 x + 3$
$= x^{4} - 2 x^{3} - 2 x^{3} - x^{3} + 3 x^{2} + 2 x^{2} + 2 x^{2} + 3 x^{2} - 4 x - 3 x - 2 x - 3 x + 4 + 3$ (Rearranging)
$= x^{4} - 5 x^{3} + 10 x^{2} - 12 x + 7$ (Combining like terms)

Thus, the answer is $x^{4} - 5 x^{3} + 10 x^{2} - 12 x + 7$ .

Suggest Corrections

Similar questions

(x^{3} - 2 x^{2} + 3 x - 4) (x - 1) - (2 x - 3) (x^{2} - x + 1)

x^{2} (x - y) y^{2} (x + 2 y)

(\frac{1}{3} x^{2} - \frac{1}{2} x + 5)

(\frac{1}{2} x^{2} - \frac{1}{3} x + 1)

l i m x \to \infty {(\frac{2 x^{2} + 3 x - 5}{3 x^{2} - 4 x + 1})}^{x + 1}

\int \frac{3 x^{2} + 4 x + 3}{(x - 2) (x^{2} + 3 x + 2)} d x

(3 x^{2} - \frac{1}{5} x + \frac{7}{3}) + (- \frac{1}{4} x^{2} + \frac{1}{3} x + \frac{1}{3} x - \frac{1}{6}) + (- 2 x^{2} - \frac{1}{2} x + 5)

Join BYJU'S Learning Program