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प्रश्न
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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उत्तर
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 x = 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 \[- 60 x^3\].
संबंधित प्रश्न
Find each of the following product:
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Find each of the following product: \[\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)\]
Evaluate each of the following when x = 2, y = −1.
\[(2xy) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)\]
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(3x2 + y2) by (2x2 + 3y2)
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(x2y − 1) (3 − 2x2y)
Simplify:
x2(x − y) y2(x + 2y)
Simplify : (2.5p − 1.5q)2 − (1.5p − 2.5q)2
Simplify : (m2 − n2m)2 + 2m3n2
Solve the following equation.
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