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I want to know the summary of multiplying monomial by mon...
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by
WinpossibleUser3664
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I WANT TO KNOW THE SUMMARY OF MULTIPLYING MONOMIAL BY MONOMIAL
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Responses
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To multiply a monomial with monomial, follow the below given steps:
• use commutative and associative properties to rearrange and group the factors.
• multiply the numerical coefficients.
• multiply powers with the same base by adding exponents.
• multiply the product obtained in just above two steps and any other variable factor by writing them with no sign between them.
For example let us take 1st monomial (aX^p)(bY^q)(cZ^r) and
2nd monomial (dX^s)(eY^t)(fZ^u)
Where a, b, c, d, e and f are the constants
X, Y, Z are the variables
p, q, r, s, t and u are the positive real numbers.
So multiplication of two monomials would be
= (aX^p)(bY^q)(cZ^r)*(dX^s)(eY^t)(fZ^u)
= (a)(X^p)(b)(Y^q)(c)(Z^r) *(d)(X^s)(e)(Y^t)(f)(Z^u)
= (a.b.c)( X^p.X^s)(Y^q.Y^t)(Z^r.Z^u)
= (abc)(X^(p+s))(Y^(q+t))(Z^(r+u))
= abc X^(p+s) Y^(q+t) Z^(r+u)
Related video lessons:
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by
Winpossible
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Aug 25, 10 10:52AM PST
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More to the above answer:-
Associative Property:
Associative property states that the change in grouping of three or more, addends or factors does not change their sum or product.
Example
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication:(4 . 5) . 10 = 4 . (5 . 10)
Commutative Property:
Commutative property states that changing the order of addends or factors does not change the sum or product.
Example
Addition: a + b = b + a
Multiplication: a × b = b × a
For more on algebra Enroll in our homework help courses
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by
Winpossible
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Aug 25, 10 02:00PM PST
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To multiply a monomial with monomial, follow the below given steps:
• use commutative and associative properties to rearrange and group the factors.
• multiply the numerical coefficients.
• multiply powers with the same base by adding exponents.
• multiply the product obtained in just above two steps and any other variable factor by writing them with no sign between them.
For example let us take 1st monomial (aX^p)(bY^q)(cZ^r) and
2nd monomial (dX^s)(eY^t)(fZ^u)
Where a, b, c, d, e and f are the constants
X, Y, Z are the variables
p, q, r, s, t and u are the positive real numbers.
So multiplication of two monomials would be
= (aX^p)(bY^q)(cZ^r)*(dX^s)(eY^t)(fZ^u)
= (a)(X^p)(b)(Y^q)(c)(Z^r) *(d)(X^s)(e)(Y^t)(f)(Z^u)
= (a.b.c)( X^p.X^s)(Y^q.Y^t)(Z^r.Z^u)
= (abc)(X^(p+s))(Y^(q+t))(Z^(r+u))
= abc X^(p+s) Y^(q+t) Z^(r+u)
Related video lessons:
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by
Winpossible
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Aug 25, 10 10:54AM PST
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