Question

Explain the Division of algebraic expression...​

Answer 1

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• In division of algebraic expression if x is a variable and m, n are positive integers such that m > n then (xᵐ ÷ xⁿ) = xm- n.

Answer 2

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Division of Algebraic Expressions is the opposite process of multiplication. In algebra, the division is similar to the division

done in arithmetic.

In division of Algebraic-Expressions, we use the

laws of exponents. There are different types of division.

1) Monomial by monomial.

2) Polynomial by monomial. 3) Polynomial by binomial.

While dividing a monomial by a monomial, we follow the following two rules:

• The coefficients of the quotient of two

monomials is equal to the quotient of their coefficients. • The variable part in the quotient of two monomials is equal to the quotient of the variables in the given monomials.

$as\:we \: know \: that \: division \: is \: the \\ inverse \: operation \: of \: multiplication$

$let \: us \: consider$

$3x \times 5x ^{3} = 15x ^{4}$

$15x^{4} \div 5x^{3} and \: 15x ^{4} \div 3x = 5x ^{3}$

$similarly \: consider \: 6a(a + 5) = 6a ^{2} + 30a$

$therefore \: (6a ^{2} + 30a ^{2} ) \div 6a = a + 5$

$and \: also \: (6a ^{2} + 3a) \div (a + 5) = 6a$