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Expand the following expression. Your answer should be a polynomial in standard form.

[tex]\left(-p^2 + 4p - 3\right)\left(p^2 + 2\right) = \square[/tex]

Sagot :

GinnyAnswer
To expand and express [tex]\(\left(-p^2 + 4p - 3\right)\left(p^2 + 2\right)\)[/tex] as a polynomial in standard form, follow these steps:

1. Distribute each term in the first polynomial [tex]\((-p^2 + 4p - 3)\)[/tex] through the second polynomial [tex]\((p^2 + 2)\)[/tex].

Let's distribute each term individually:

- Distribute [tex]\(-p^2\)[/tex] through [tex]\((p^2 + 2)\)[/tex]:

[tex]\[ -p^2(p^2 + 2) = -p^2 \cdot p^2 + (-p^2 \cdot 2) = -p^4 - 2p^2 \][/tex]

- Distribute [tex]\(4p\)[/tex] through [tex]\((p^2 + 2)\)[/tex]:

[tex]\[ 4p(p^2 + 2) = 4p \cdot p^2 + 4p \cdot 2 = 4p^3 + 8p \][/tex]

- Distribute [tex]\(-3\)[/tex] through [tex]\((p^2 + 2)\)[/tex]:

[tex]\[ -3(p^2 + 2) = -3 \cdot p^2 + (-3 \cdot 2) = -3p^2 - 6 \][/tex]

2. Combine all the distributed parts:

[tex]\[ -p^4 - 2p^2 + 4p^3 + 8p - 3p^2 - 6 \][/tex]

3. Combine like terms to simplify the expression:

[tex]\[ -p^4 + 4p^3 - 5p^2 + 8p - 6 \][/tex]

Thus, the polynomial in standard form is:

[tex]\[ \left(-p^2 + 4p - 3\right)\left(p^2 + 2\right) = -p^4 + 4p^3 - 5p^2 + 8p - 6 \][/tex]
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