IDNLearn.com makes it easy to get reliable answers from experts and enthusiasts alike. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

Simplify the expression [tex]-3(x+3)^2-3+3x[/tex]. What is the simplified expression in standard form?

A. [tex]-3x^2-18x-27[/tex]
B. [tex]-3x^2-15x-30[/tex]
C. [tex]-3x^2+3x+6[/tex]
D. [tex]-3x^2+3x-30[/tex]


Sagot :

To simplify the expression [tex]\(-3(x+3)^2 - 3 + 3x\)[/tex] and present it in standard form, we can follow these steps:

1. Expand [tex]\((x+3)^2\)[/tex]:

The term [tex]\((x+3)^2\)[/tex] can be expanded using the binomial formula:
[tex]\[ (x+3)^2 = x^2 + 6x + 9 \][/tex]

So, replace [tex]\((x+3)^2\)[/tex] with this expanded form:
[tex]\[ -3(x^2 + 6x + 9) - 3 + 3x \][/tex]

2. Distribute the [tex]\(-3\)[/tex] across the terms inside the parentheses:

Distribute [tex]\(-3\)[/tex] through [tex]\(x^2 + 6x + 9\)[/tex]:
[tex]\[ -3(x^2 + 6x + 9) = -3x^2 - 18x - 27 \][/tex]

Now, plug this result back into the expression:
[tex]\[ -3x^2 - 18x - 27 - 3 + 3x \][/tex]

3. Combine like terms:

Combine the constants and the linear terms:
[tex]\[ -3x^2 - 18x + 3x - 27 - 3 \][/tex]

Simplify by combining [tex]\(-18x\)[/tex] and [tex]\(3x\)[/tex]:
[tex]\[ -18x + 3x = -15x \][/tex]

Combine the constants [tex]\(-27\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[ -27 - 3 = -30 \][/tex]

So, the expression simplifies to:
[tex]\[ -3x^2 - 15x - 30 \][/tex]

4. Conclusion:

The given expression [tex]\(-3(x+3)^2 - 3 + 3x\)[/tex] simplifies to the standard form:
[tex]\[ -3x^2 - 15x - 30 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{-3x^2 - 15x - 30} \][/tex]