"Question 4 Obtain the volume of rectangular boxes with the following length, breadth and height respectively. (i) 5a, 3a^2, 7a^4 (ii) 2p, 4q, 8r (iii) xy, 2x^2y, 2xy^2 (iv) a, 2b, 3c
Class 8 Algebraic Expressions and Identities Page 144"
Answers
Algebraic expressions:
A combination of constants and variables connected by any or all of the four fundamental operations +, -,×,÷ is called an algebraic expression.
Terms:
The different parts of the expression separated by the sign+ or – are called the terms of the expression.
Monomials:
A monomial is a one term algebraic expression .
Multiplication of algebraic expression:
The product of two factors with like signs is positive and the product of two factors with unlike signs is negative.
Multiplication of monomials:
The coefficient of the product of two monomials is equal to the product of their coefficients and the variable part in the product is equal to the product of the variable in the given monomials.
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Solution:
We know that
Volume = length x breadth x height
(i) 5a x 3a² x 7a^4 = (5x 3x 7 ) x(a xa² xa^4 )
volume =105a^7
(ii) 2p x 4q x 8r = (2x 4x 8 )x ( px q x r)
volume = 64pqr
(iii) xy x 2x²y x 2xy² = (2x2 ) x (xy x²y xy²)
volume= 4x⁴y⁴
(iv) a x 2b x 3c = (2x 3) x ( a x b x c)
volume= 6abc
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Hope this will help you....