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# Express Each of the Following Product as a Monomials and Verify the Result in Each Case for X = 1: (X2)3 × (2x) × (−4x) × (5) - Mathematics

Answer in Brief

Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)

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#### Solution

We have to find the product of the expression in order to express it as a monomial.
To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​ $a^m \times a^n = a^{m + n} \text { and } \left( a^m \right)^n = a^{mn}$

We have:

$\left( x^2 \right)^3 \times \left( 2x \right) \times \left( - 4x \right) \times 5$

$= \left( x^6 \right) \times \left( 2x \right) \times \left( - 4x \right) \times 5$

$= \left\{ 2 \times \left( - 4 \right) \times 5 \right\} \times \left( x^6 \times x \times x \right)$

$= \left\{ 2 \times \left( - 4 \right) \times 5 \right\} \times \left( x^{6 + 1 + 1} \right)$

$= - 40 x^8$

$\therefore$ $\left( x^2 \right)^3 \times \left( 2x \right) \times \left( - 4x \right) \times 5 = - 40 x^8$

Substituting x = 1 in LHS, we get:​

$\text { LHS } { = \left( x^2 \right)^3 \times \left( 2x \right) \times \left( - 4x \right) \times 5$

$= \left( 1^2 \right)^3 \times \left( 2 \times 1 \right) \times \left( - 4 \times 1 \right) \times 5$

$= 1^6 \times 2 \times \left( - 4 \right) \times 5$

$= 1 \times 2 \times \left( - 4 \right) \times 5$

$= - 40$

Putting x = 1 in RHS, we get:​

$\text { RHS } = - 40 x^8$

$= - 40 \left( 1 \right)^8$

$= - 40 \times 1$

$= - 40$

$\because$ LHS = RHS for = 1; therefore, the result is correct

Thus, the answer is $- 40 x^8$.

Concept: Multiplication of Algebraic Expressions
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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.3 | Q 21 | Page 14
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