Answer :
To simplify the expression
[tex]$$-4x^2(3x-7),$$[/tex]
we distribute the term [tex]$-4x^2$[/tex] to both terms inside the parentheses.
Step 1. Multiply [tex]$-4x^2$[/tex] by [tex]$3x$[/tex]:
[tex]$$-4x^2 \cdot 3x = -12x^{2+1} = -12x^3.$$[/tex]
Step 2. Multiply [tex]$-4x^2$[/tex] by [tex]$-7$[/tex]:
[tex]$$-4x^2 \cdot (-7) = 28x^2.$$[/tex]
Step 3. Combine the two results:
[tex]$$-12x^3 + 28x^2.$$[/tex]
Thus, the simplified expression is
[tex]$$-12x^3+28x^2,$$[/tex]
which corresponds to option C.
[tex]$$-4x^2(3x-7),$$[/tex]
we distribute the term [tex]$-4x^2$[/tex] to both terms inside the parentheses.
Step 1. Multiply [tex]$-4x^2$[/tex] by [tex]$3x$[/tex]:
[tex]$$-4x^2 \cdot 3x = -12x^{2+1} = -12x^3.$$[/tex]
Step 2. Multiply [tex]$-4x^2$[/tex] by [tex]$-7$[/tex]:
[tex]$$-4x^2 \cdot (-7) = 28x^2.$$[/tex]
Step 3. Combine the two results:
[tex]$$-12x^3 + 28x^2.$$[/tex]
Thus, the simplified expression is
[tex]$$-12x^3+28x^2,$$[/tex]
which corresponds to option C.