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Given:
[tex]\[ C = 3y^2 + 4y + 4 \][/tex]
[tex]\[ D = -7y^2 + 3y - 6 \][/tex]

Calculate [tex]\( D - C \)[/tex].

Your answer should be a polynomial in standard form.

Sagot :

GinnyAnswer
To find the polynomial [tex]\(D - C\)[/tex], we'll subtract polynomial [tex]\(C\)[/tex] from polynomial [tex]\(D\)[/tex]. Let's denote the given polynomials first:

[tex]\[ C = 3y^2 + 4y + 4 \][/tex]
[tex]\[ D = -7y^2 + 3y - 6 \][/tex]

Now we need to calculate [tex]\(D - C\)[/tex]:

[tex]\[ D - C = (-7y^2 + 3y - 6) - (3y^2 + 4y + 4) \][/tex]

To simplify this, distribute the negative sign through the polynomial [tex]\(C\)[/tex]:

[tex]\[ D - C = -7y^2 + 3y - 6 - 3y^2 - 4y - 4 \][/tex]

Next, combine like terms:

1. Combine the [tex]\(y^2\)[/tex] terms:
[tex]\[ -7y^2 - 3y^2 = -10y^2 \][/tex]

2. Combine the [tex]\(y\)[/tex] terms:
[tex]\[ 3y - 4y = -y \][/tex]

3. Combine the constant terms:
[tex]\[ -6 - 4 = -10 \][/tex]

Putting it all together, we get the resultant polynomial:

[tex]\[ D - C = -10y^2 - y - 10 \][/tex]

Thus, the polynomial [tex]\(D - C\)[/tex] in standard form is:

[tex]\[ \boxed{-10y^2 - y - 10} \][/tex]
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