Answer :
To simplify the expression
[tex]$$
-4x^2(3x - 7),
$$[/tex]
we need to distribute [tex]$-4x^2$[/tex] to each term inside the parentheses:
1. Multiply [tex]$-4x^2$[/tex] by [tex]$3x$[/tex]:
- The coefficients: [tex]$-4 \times 3 = -12$[/tex].
- The variable part: [tex]$x^2 \times x = x^{2+1} = x^3$[/tex].
This gives the term:
[tex]$$-12x^3.$$[/tex]
2. Multiply [tex]$-4x^2$[/tex] by [tex]$-7$[/tex]:
- The coefficients: [tex]$-4 \times -7 = 28$[/tex].
- The variable part remains [tex]$x^2$[/tex].
This gives the term:
[tex]$$28x^2.$$[/tex]
Putting the two terms together, the simplified expression is:
[tex]$$
-12x^3 + 28x^2.
$$[/tex]
This corresponds to option B.
[tex]$$
-4x^2(3x - 7),
$$[/tex]
we need to distribute [tex]$-4x^2$[/tex] to each term inside the parentheses:
1. Multiply [tex]$-4x^2$[/tex] by [tex]$3x$[/tex]:
- The coefficients: [tex]$-4 \times 3 = -12$[/tex].
- The variable part: [tex]$x^2 \times x = x^{2+1} = x^3$[/tex].
This gives the term:
[tex]$$-12x^3.$$[/tex]
2. Multiply [tex]$-4x^2$[/tex] by [tex]$-7$[/tex]:
- The coefficients: [tex]$-4 \times -7 = 28$[/tex].
- The variable part remains [tex]$x^2$[/tex].
This gives the term:
[tex]$$28x^2.$$[/tex]
Putting the two terms together, the simplified expression is:
[tex]$$
-12x^3 + 28x^2.
$$[/tex]
This corresponds to option B.
