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) = nā¶+7mnāµ+14mĀ²nā“-5mĀ³nĀ³-6mā¶-2mā¶
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,
8mnāµ-2mā¶+5mĀ²nā“-mĀ³nĀ³+nā¶-4mā¶+9mĀ²nā“-mnāµ-4mĀ³nĀ³
Let the above polynomial is. Thus,
f(m,n) = 8mnāµ-2mā¶+5mĀ²nā“-mĀ³nĀ³+nā¶-4mā¶+9mĀ²nā“-mnāµ-4mĀ³nĀ³
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) = ( 8mnāµ - mnāµ ) -2mā¶ + ( 5mĀ²nā“+9mĀ²nā“ ) - ( mĀ³nĀ³-4mĀ³nĀ³) + nā¶-4mā¶
f(m,n) = 7mnāµ - 2mā¶ + 14 mĀ²nā“ - 5 mĀ³nĀ³ + nā¶- 6mā¶
Arrange it as,
f(m,n) = nā¶+7mnāµ+14mĀ²nā“-5mĀ³nĀ³-6mā¶-2mā¶
Thus the polynomial correctly combines the like terms and expresses the given polynomial in standard form is,
f(m,n) = nā¶+7mnāµ+14mĀ²nā“-5mĀ³nĀ³-6mā¶-2mā¶
Learn more about the polynomial equation here;
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