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Write as a polynomial - \dfrac{ 2 }{ 7 } { a }^{ 2 } { y }^{ 7 } \left( 5a { y }^{ 2 } - \dfrac{ 1 }{ 2 } { a }^{ 2 } y- \dfrac{ 5 }{ 6 } { a }^{ 3 } \right)

User Ruba
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4 votes

Answer:


(10)/(7)\cdot a^(3)\cdot y^(4) - (1)/(7)\cdot a^(4)\cdot y^(3) - (5)/(21)\cdot a^5\cdot y^(2)}

Explanation:

According to the statement, we have the algebraic equation
(2)/(7)\cdot {a^(2)\cdot y^(2)}\cdot \left(5\cdot a\cdot y^(2) - (1)/(2)\cdot {a}^(2)\cdot y - (5)/(6)\cdot a^(3)\right) and we must to rewrite it as a polynomial. Since there are two variables:
a,
y, we must observe the following definition of polynomial:


p(a, y) = \Sigma\limits_(i = 0)^(n) c_(i)\cdot a^(i)\cdot y^(n-i) (1)

Where:


i - Index.


c_(i) - i-th Coefficient of the polynomial.


n - Grade of the polynomial.

By means of algebraic handling, we have the following result:

1)
(2)/(7)\cdot {a^(2)\cdot y^(2)}\cdot \left(5\cdot a\cdot y^(2) - (1)/(2)\cdot {a}^(2)\cdot y - (5)/(6)\cdot a^(3)\right) Given

2)
\left((2)/(7)\cdot a^(2)\cdot y^(2) \right)\cdot \left(5\cdot a\cdot y^(2)\right) + \left((2)/(7)\cdot a^(2)\cdot y^(2) \right) \cdot \left(-(1)/(2)\cdot a^(2)\cdot y \right) + \left((2)/(7)\cdot a^(2)\cdot y^(2) \right)\cdot \left(-(5)/(6)\cdot a^(3)\right) Associative and distributive properties/
(-a)\cdot b = -a\cdot b

3)
(10)/(7)\cdot a^(3)\cdot y^(4) - (1)/(7)\cdot a^(4)\cdot y^(3) - (5)/(21)\cdot a^5\cdot y^(2)} Associative and commutative properties/
(a)/(b)* (c)/(d) = (a\cdot c)/(b\cdot d)/
(-a)\cdot b = -a\cdot b/Definition of subtraction/
(a\cdot c)/(b\cdot c) = (a)/(b)/Result

User Cjerez
by
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