Answer :
To simplify
[tex]$$7x^2\left(6x + 3x^2 - 4\right),$$[/tex]
we distribute [tex]$7x^2$[/tex] to each term inside the parentheses.
1. Multiply [tex]$7x^2$[/tex] by [tex]$6x$[/tex]:
[tex]$$7x^2 \cdot 6x = 42x^3.$$[/tex]
2. Multiply [tex]$7x^2$[/tex] by [tex]$3x^2$[/tex]:
[tex]$$7x^2 \cdot 3x^2 = 21x^4.$$[/tex]
3. Multiply [tex]$7x^2$[/tex] by [tex]$-4$[/tex]:
[tex]$$7x^2 \cdot (-4) = -28x^2.$$[/tex]
Now, combine all the terms:
[tex]$$21x^4 + 42x^3 - 28x^2.$$[/tex]
Thus, the correct simplification is:
[tex]$$\boxed{21x^4 + 42x^3 - 28x^2}.$$[/tex]
[tex]$$7x^2\left(6x + 3x^2 - 4\right),$$[/tex]
we distribute [tex]$7x^2$[/tex] to each term inside the parentheses.
1. Multiply [tex]$7x^2$[/tex] by [tex]$6x$[/tex]:
[tex]$$7x^2 \cdot 6x = 42x^3.$$[/tex]
2. Multiply [tex]$7x^2$[/tex] by [tex]$3x^2$[/tex]:
[tex]$$7x^2 \cdot 3x^2 = 21x^4.$$[/tex]
3. Multiply [tex]$7x^2$[/tex] by [tex]$-4$[/tex]:
[tex]$$7x^2 \cdot (-4) = -28x^2.$$[/tex]
Now, combine all the terms:
[tex]$$21x^4 + 42x^3 - 28x^2.$$[/tex]
Thus, the correct simplification is:
[tex]$$\boxed{21x^4 + 42x^3 - 28x^2}.$$[/tex]
