the sum of two polynomials is $8d^{5}-3c^{3}d^{2}+5c^{2}d^{3}-4cd^{4}+9$. if one addend is…

the sum of two polynomials is $8d^{5}-3c^{3}d^{2}+5c^{2}d^{3}-4cd^{4}+9$. if one addend is $2d^{5}-c^{3}d^{2}+8cd^{4}+1$, what is the other addend?\n$6d^{5}-2c^{3}d^{2}+5c^{2}d^{3}-12cd^{4}+8$\n$6d^{5}-4c^{3}d^{2}+3c^{2}d^{3}-4cd^{4}+8$\n$6d^{5}-4c^{3}d^{2}+5c^{2}d^{3}-12cd^{4}+8$\n$6d^{5}-2c^{3}d^{2}-3c^{2}d^{3}-4cd^{4}+8$

the sum of two polynomials is $8d^{5}-3c^{3}d^{2}+5c^{2}d^{3}-4cd^{4}+9$. if one addend is $2d^{5}-c^{3}d^{2}+8cd^{4}+1$, what is the other addend?\n$6d^{5}-2c^{3}d^{2}+5c^{2}d^{3}-12cd^{4}+8$\n$6d^{5}-4c^{3}d^{2}+3c^{2}d^{3}-4cd^{4}+8$\n$6d^{5}-4c^{3}d^{2}+5c^{2}d^{3}-12cd^{4}+8$\n$6d^{5}-2c^{3}d^{2}-3c^{2}d^{3}-4cd^{4}+8$

Answer

Explanation:

Step1: Recall the relationship

Let the sum of two polynomials be $S$, one addend be $A$ and the other be $B$. Then $S = A + B$, so $B=S - A$. Here, $S = 8d^{5}-3c^{3}d^{2}+5c^{2}d^{3}-4cd^{4}+9$ and $A = 2d^{5}-c^{3}d^{2}+8cd^{4}+1$.

Step2: Subtract like - terms

Subtract the coefficients of like - terms: For the $d^{5}$ term: $(8 - 2)d^{5}=6d^{5}$; For the $c^{3}d^{2}$ term: $(-3-(- 1))c^{3}d^{2}=(-3 + 1)c^{3}d^{2}=-2c^{3}d^{2}$; For the $c^{2}d^{3}$ term: $5c^{2}d^{3}$ remains the same as there is no like - term in $A$; For the $cd^{4}$ term: $(-4 - 8)cd^{4}=-12cd^{4}$; For the constant term: $(9 - 1)=8$.

Answer:

$6d^{5}-2c^{3}d^{2}+5c^{2}d^{3}-12cd^{4}+8$ (corresponds to the first option)