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प्रश्न
Simplify:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)
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उत्तर
To simplify,we will proceed as follows:
\[\left( x^3 - 2 x^2 + 3x - 4 \right)\left( x - 1 \right) - \left( 2x - 3 \right)\left( x^2 - x + 1 \right)\]
\[ = \left[ \left( x^3 - 2 x^2 + 3x - 4 \right)\left( x - 1 \right) \right] - \left[ \left( 2x - 3 \right)\left( x^2 - x + 1 \right) \right]\]
\[= \left[ x\left( x^3 - 2 x^2 + 3x - 4 \right) - 1\left( x^3 - 2 x^2 + 3x - 4 \right) \right] - \left[ 2x\left( x^2 - x + 1 \right) - 3\left( x^2 - x + 1 \right) \right]\] (Distributive law)
\[= \left[ x\left( x^3 - 2 x^2 + 3x - 4 \right) - 1\left( x^3 - 2 x^2 + 3x - 4 \right) \right] - \left[ 2x\left( x^2 - x + 1 \right) - 3\left( x^2 - x + 1 \right) \right]\]
\[ = x^4 - 2 x^3 + 3 x^2 - 4x - x^3 + 2 x^2 - 3x + 4 - \left[ 2 x^3 - 2 x^2 + 2x - 3 x^2 + 3x - 3 \right]\]
\[ = x^4 - 2 x^3 + 3 x^2 - 4x - x^3 + 2 x^2 - 3x + 4 - 2 x^3 + 2 x^2 - 2x + 3 x^2 - 3x + 3\]
\[= x^4 - 2 x^3 - 2 x^3 - x^3 + 3 x^2 + 2 x^2 + 2 x^2 + 3 x^2 - 4x - 3x - 2x - 3x + 4 + 3\]
(Rearranging)
\[= x^4 - 5 x^3 + 10 x^2 - 12x + 7\] (Combining like terms)
Thus, the answer is \[x^4 - 5 x^3 + 10 x^2 - 12x + 7\].
संबंधित प्रश्न
Find each of the following product: \[\left( \frac{- 24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)\]
Find each of the following product:
\[\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x2) × (−3x) × \[\left( \frac{4}{5} x^3 \right)\]
Simplify: x3y(x2 − 2x) + 2xy(x3 − x4)
Simplify: a(b − c) + b(c − a) + c(a − b)
Multiply:
(7x + y) by (x + 5y)
Multiply:
[−3d + (−7f)] by (5d + f)
Simplify:
(x3 − 2x2 + 5x − 7)(2x − 3)
Show that: (4pq + 3q)2 − (4pq − 3q)2 = 48pq2
Multiply:
(12a + 17b) × 4c
