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

A. [tex]30x^4-20x^3+15x^2[/tex]

B. [tex]-11x^4-x^3-8x^2[/tex]

C. [tex]-30x^4+20x^3-15x^2[/tex]

D. [tex]30x^4+20x^3+15x^2[/tex]



Answer :

To simplify the expression [tex]\(-5 x^2 (4x - 6x^2 - 3)\)[/tex], we need to distribute [tex]\(-5 x^2\)[/tex] to each term inside the parentheses. Let's break it down step by step:

1. Start with the expression:
[tex]\[ -5 x^2 (4x - 6x^2 - 3) \][/tex]

2. Distribute [tex]\(-5 x^2\)[/tex] to each term inside the parentheses:
[tex]\[ = (-5 x^2) \cdot (4x) + (-5 x^2) \cdot (-6x^2) + (-5 x^2) \cdot (-3) \][/tex]

3. Multiply each term:
[tex]\[ (-5 x^2) \cdot (4x) = -20 x^3 \][/tex]
[tex]\[ (-5 x^2) \cdot (-6x^2) = 30 x^4 \][/tex]
[tex]\[ (-5 x^2) \cdot (-3) = 15 x^2 \][/tex]

4. Combine all the terms:
[tex]\[ 30 x^4 - 20 x^3 + 15 x^2 \][/tex]

So, the simplified expression is:
[tex]\[ 30 x^4 - 20 x^3 + 15 x^2 \][/tex]

This matches the first option given. Therefore, the correct simplification is:
[tex]\[ \boxed{30 x^4 - 20 x^3 + 15 x^2} \][/tex]