4. [tex]\((06.04 \, LC)\)[/tex]

Choose the correct simplification of the expression [tex]\(-3x^2(5x - 4x^2 - 6)\)[/tex].

A. [tex]\(12x^4 + 15x^3 + 18x^2\)[/tex]
B. [tex]\(-7x^4 + 2x^3 - 9x^2\)[/tex]
C. [tex]\(12x^4 - 15x^3 + 18x^2\)[/tex]
D. [tex]\(-12x^4 + 15x^3 - 18x^2\)[/tex]



Answer :

Let's simplify the expression [tex]\(-3x^2(5x - 4x^2 - 6)\)[/tex] step by step:

1. Identify the terms inside the parentheses:
The terms inside the parentheses are [tex]\(5x\)[/tex], [tex]\(-4x^2\)[/tex], and [tex]\(-6\)[/tex].

2. Apply the distributive property:
This means we will multiply [tex]\(-3x^2\)[/tex] by each term inside the parentheses individually.

- First, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[ -3x^2 \cdot 5x = -15x^3 \][/tex]

- Next, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(-4x^2\)[/tex]:
[tex]\[ -3x^2 \cdot -4x^2 = 12x^4 \][/tex]
Notice that the multiplication of two negative numbers results in a positive number.

- Finally, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[ -3x^2 \cdot -6 = 18x^2 \][/tex]
Again, the multiplication of two negative numbers results in a positive number.

3. Combine the results:
We now gather all the terms obtained from the distributive property:
[tex]\[ 12x^4 - 15x^3 + 18x^2 \][/tex]

Therefore, the correct simplification of the expression [tex]\(-3x^2(5x - 4x^2 - 6)\)[/tex] is:
[tex]\[ \boxed{12x^4 - 15x^3 + 18x^2} \][/tex]

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