Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 - 2m6+5m²n4 - m³n³ + n6 - 4m6 + 9m²n4 - mn5 - 4m³n³ O n6 + 7mn5 + 14m²n4 - 5m³n³ - 6m6 O -2m6 - 5m³n³ + 14m²n4 + 7mn5 + n6 O 14m²n4 + 7mn5 - 6m6 - 5m³n³ + n° On6 - 6m6 + 7mn5 + 14m²n4 - 5m³n³ Mark this and return Next Submi Sa Exitve an
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08-06-2022
Mathematics

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Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 - 2m6+5m²n4 - m³n³ + n6 - 4m6 + 9m²n4 - mn5 - 4m³n³ O n6 + 7mn5 + 14m²n4 - 5m³n³ - 6m6 O -2m6 - 5m³n³ + 14m²n4 + 7mn5 + n6 O 14m²n4 + 7mn5 - 6m6 - 5m³n³ + n° On6 - 6m6 + 7mn5 + 14m²n4 - 5m³n³ Mark this and return Next Submi Sa Exitve an
d

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 1 · 2022-06-15T12:37:13+02:00

Option A is the correct option. The polynomial correctly combines the like terms and expresses the given polynomial in standard form is,

f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶

What is the polynomial equation?

A polynomial equation is an equation in which the unknown variable is one and the highest power of the unknown variable is n. Here n can be any real number.

Given information-

The polynomial equation given in the problem is,

8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³

Let the above polynomial is. Thus,

f(m,n) = 8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³

The terms with the same base and exponents can be added or subtracted from each other. Thus solve the equation further as,

f(m,n) = ( 8mn⁵ - mn⁵ ) -2m⁶ + ( 5m²n⁴+9m²n⁴ ) - ( m³n³-4m³n³) + n⁶-4m⁶

f(m,n) = 7mn⁵ - 2m⁶ + 14 m²n⁴ - 5 m³n³ + n⁶- 6m⁶

Arrange it as,

f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶

Thus the polynomial correctly combines the like terms and expresses the given polynomial in standard form is,

f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶

Learn more about the polynomial equation here;

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