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Simplify: (X3 − 2x2 + 3x − 4) (X −1) − (2x − 3)(X2 − X + 1) - Mathematics

Answer in Brief

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

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Solution

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 \[x^4 - 5 x^3 + 10 x^2 - 12x + 7\].

Concept: Multiplication of Algebraic Expressions
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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.5 | Q 32 | Page 31
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