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Simplify: (X3 − 2x2 + 5x − 7)(2x − 3) - Mathematics

Answer in Brief

Simplify:
(x3 − 2x2 + 5x − 7)(2x − 3)

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Solution

To simplify, we will proceed as follows:

\[\left( x^3 - 2 x^2 + 5x - 7 \right)\left( 2x - 3 \right)\]

\[ = 2x\left( x^3 - 2 x^2 + 5x - 7 \right) - 3\left( x^3 - 2 x^2 + 5x - 7 \right)\]

\[ = 2 x^4 - 4 x^3 + 10 x^2 - 14x - 3 x^3 + 6 x^2 - 15x + 21\]

\[= 2 x^4 - 4 x^3 - 3 x^3 + 10 x^2 + 6 x^2 - 14x - 15x + 21\]   (Rearranging)

\[= 2 x^4 - 7 x^3 + 16 x^2 - 29x + 21\]   (Combining like terms)
Thus, the answer is \[2 x^4 - 7 x^3 + 16 x^2 - 29x + 21\].

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 24 | Page 31
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