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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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