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Simplify [tex]\left(3 x^2 - 3 + 9 x^3\right) - \left(4 x^3 - 2 x^2 + 16\right)[/tex]

A. [tex]x^3 - 5 x^2 + 25[/tex]
B. [tex]-x^3 + x^2 - 25[/tex]
C. [tex]5 x^3 + x^2 + 13[/tex]
D. [tex]5 x^3 + 5 x^2 - 19[/tex]

Sagot :

GinnyAnswer
Certainly! Let's simplify the given expression step by step. We start with:

[tex]\[ \left(3x^2 - 3 + 9x^3\right) - \left(4x^3 - 2x^2 + 16\right) \][/tex]

First, we distribute the negative sign across the terms in the second polynomial:

[tex]\[ = 3x^2 - 3 + 9x^3 - 4x^3 + 2x^2 - 16 \][/tex]

Next, we combine like terms. We start by combining the [tex]\(x^3\)[/tex] terms:

[tex]\[ 9x^3 - 4x^3 = 5x^3 \][/tex]

Then, we combine the [tex]\(x^2\)[/tex] terms:

[tex]\[ 3x^2 + 2x^2 = 5x^2 \][/tex]

Finally, we combine the constant terms:

[tex]\[ -3 - 16 = -19 \][/tex]

Putting all the simplified terms together, we get:

[tex]\[ 5x^3 + 5x^2 - 19 \][/tex]

Therefore, the simplified expression is:

[tex]\[ \boxed{5x^3 + 5x^2 - 19} \][/tex]
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