Answer :
To simplify the expression
[tex]$$
9x^2 \left(4x + 2x^2 - 1\right),
$$[/tex]
we use the distributive property by multiplying each term inside the parentheses by [tex]$9x^2$[/tex]:
1. Multiply [tex]$9x^2$[/tex] by [tex]$4x$[/tex]:
[tex]$$
9x^2 \cdot 4x = 36x^3.
$$[/tex]
2. Multiply [tex]$9x^2$[/tex] by [tex]$2x^2$[/tex]:
[tex]$$
9x^2 \cdot 2x^2 = 18x^4.
$$[/tex]
3. Multiply [tex]$9x^2$[/tex] by [tex]$-1$[/tex]:
[tex]$$
9x^2 \cdot (-1) = -9x^2.
$$[/tex]
Now, arranging the terms in descending order of the exponents, we obtain:
[tex]$$
18x^4 + 36x^3 - 9x^2.
$$[/tex]
Thus, the correct simplification is
[tex]$$
\boxed{18x^4+36x^3-9x^2}.
$$[/tex]]
[tex]$$
9x^2 \left(4x + 2x^2 - 1\right),
$$[/tex]
we use the distributive property by multiplying each term inside the parentheses by [tex]$9x^2$[/tex]:
1. Multiply [tex]$9x^2$[/tex] by [tex]$4x$[/tex]:
[tex]$$
9x^2 \cdot 4x = 36x^3.
$$[/tex]
2. Multiply [tex]$9x^2$[/tex] by [tex]$2x^2$[/tex]:
[tex]$$
9x^2 \cdot 2x^2 = 18x^4.
$$[/tex]
3. Multiply [tex]$9x^2$[/tex] by [tex]$-1$[/tex]:
[tex]$$
9x^2 \cdot (-1) = -9x^2.
$$[/tex]
Now, arranging the terms in descending order of the exponents, we obtain:
[tex]$$
18x^4 + 36x^3 - 9x^2.
$$[/tex]
Thus, the correct simplification is
[tex]$$
\boxed{18x^4+36x^3-9x^2}.
$$[/tex]]
