College

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

A. [tex]$21 x^4-42 x^3+28 x^2$[/tex]

B. [tex]$42 x^4+21 x^3-3 x^2$[/tex]

C. [tex]$21 x^4+42 x^3-28 x^2$[/tex]

D. [tex]$42 x^4-13 x^3+11 x^2$[/tex]

Answer :

We start with the expression

[tex]$$7x^2\left(6x + 3x^2 - 4\right).$$[/tex]

Step 1: Distribute [tex]$7x^2$[/tex] to each term inside the parentheses.

Multiply [tex]$7x^2$[/tex] by each term:

- Multiply [tex]$7x^2$[/tex] by [tex]$6x$[/tex]:

[tex]$$7x^2 \cdot 6x = 42x^3.$$[/tex]

- Multiply [tex]$7x^2$[/tex] by [tex]$3x^2$[/tex]:

[tex]$$7x^2 \cdot 3x^2 = 21x^4.$$[/tex]

- Multiply [tex]$7x^2$[/tex] by [tex]$-4$[/tex]:

[tex]$$7x^2 \cdot (-4) = -28x^2.$$[/tex]

Step 2: Combine the results.

After distributing, we have:

[tex]$$21x^4 + 42x^3 - 28x^2.$$[/tex]

Thus, the simplified expression is

[tex]$$21x^4 + 42x^3 - 28x^2.$$[/tex]

This corresponds to the third option among the given choices.

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