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

A. [tex]$21x^4 - 42x^3 + 28x^2$[/tex]
B. [tex]$42x^4 + 21x^3 - 3x^2$[/tex]
C. [tex]$21x^4 + 42x^3 - 28x^2$[/tex]
D. [tex]$42x^4 - 13x^3 + 11x^2$[/tex]

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]

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