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

Answer in Brief

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

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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 law of indices, i.e.,​ \[a^m \times a^n = a^{m + n}\].

We have: 

\[\left( 3x \right) \times \left( 4x \right) \times \left( - 5x \right)\]

\[ = \left\{ 3 \times 4 \times \left( - 5 \right) \right\} \times \left( x \times x \times x \right)\]

\[ = \left\{ 3 \times 4 \times \left( - 5 \right) \right\} \times \left( x^{1 + 1 + 1} \right)\]

\[ = - 60 x^3\]

Substituting x = 1 in LHS, we get:

\[LHS = \left( 3x \right) \times \left( 4x \right) \times \left( - 5x \right)\]

\[ = \left( 3 \times 1 \right) \times \left( 4 \times 1 \right) \times \left( - 5 \times 1 \right)\]

\[ = - 60\]

Putting = 1 in RHS, we get:

\[\text { RHS } = - 60 x^3 \]

\[ = - 60 \left( 1 \right)^3 \]

\[ = - 60 \times 1\]

\[ = - 60\]

\[\because\] LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is \[- 60 x^3\].

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 18 | Page 14
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