Choose the correct simplification of [tex]$7 x^2\left(6 x+3 x^2-4\right)$[/tex].

A. [tex]$21 x^4-42 x^3+28 x^2$[/tex]

B. [tex][tex]$42 x^4+21 x^3-3 x^2$[/tex][/tex]

C. [tex]$21 x^4+42 x^3-28 x^2$[/tex]

D. [tex]$42 x^4-13 x^3+11 x^2$[/tex]



Answer :

To simplify the expression [tex]\( 7 x^2(6 x + 3 x^2 - 4) \)[/tex], let's follow each step carefully:

1. Distribute [tex]\( 7 x^2 \)[/tex] to each term inside the parentheses:

[tex]\[ 7 x^2 \cdot 6 x + 7 x^2 \cdot 3 x^2 - 7 x^2 \cdot 4 \][/tex]

2. Calculate each term separately:

- For the first term [tex]\( 7 x^2 \cdot 6 x \)[/tex]:
[tex]\[ 7 x^2 \cdot 6 x = 42 x^3 \][/tex]

- For the second term [tex]\( 7 x^2 \cdot 3 x^2 \)[/tex]:
[tex]\[ 7 x^2 \cdot 3 x^2 = 21 x^4 \][/tex]

- For the third term [tex]\( 7 x^2 \cdot 4 \)[/tex]:
[tex]\[ 7 x^2 \cdot 4 = 28 x^2 \][/tex]

3. Combine the terms:

After distributing and simplifying each term, we get:
[tex]\[ 42 x^3 + 21 x^4 - 28 x^2 \][/tex]

4. Rearrange the terms in standard polynomial form (highest degree first):

[tex]\[ 21 x^4 + 42 x^3 - 28 x^2 \][/tex]

Thus, the correct simplification of [tex]\( 7 x^2(6 x + 3 x^2 - 4) \)[/tex] is:

[tex]\[ \boxed{21 x^4 + 42 x^3 - 28 x^2} \][/tex]