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Your answer should be a polynomial in standard form.

[tex]\ \textless \ br/\ \textgreater \ \left(d^2 + 6d + 9\right) - \left(d^3 + 6d + 9\right) =\ \textless \ br/\ \textgreater \ [/tex]

[tex]\ \textless \ br/\ \textgreater \ \square\ \textless \ br/\ \textgreater \ [/tex]

Sagot :

GinnyAnsweridn
Sure! Let's solve this step by step.

We are given the expression:

[tex]\[ \left(d^2 + 6d + 9\right) - \left(d^3 + 6d + 9\right) \][/tex]

First, let's distribute the negative sign across the second polynomial:

[tex]\[ d^2 + 6d + 9 - d^3 - 6d - 9 \][/tex]

Now, we combine like terms by grouping the corresponding powers of [tex]\(d\)[/tex]:

1. For [tex]\(d^3\)[/tex]:
[tex]\[ -d^3 \][/tex]

2. For [tex]\(d^2\)[/tex]:
[tex]\[ +d^2 \][/tex]

3. For [tex]\(d^1\)[/tex]:
[tex]\[ 6d - 6d = 0 \][/tex]

4. For the constant term:
[tex]\[ 9 - 9 = 0 \][/tex]

So, putting it all together:

[tex]\[ -d^3 + d^2 \][/tex]

This is the polynomial result in the standard form.

Thus,

[tex]\[ \left(d^2 + 6d + 9\right) - \left(d^3 + 6d + 9\right) = d^2(1 - d) \][/tex]
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