Question

Which expression is equivalent to 2(3x+4)(x−1)(x−3)

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Responses

A 6x3−16x2−14x+24
6 x cubed minus 16 x squared minus 14 x plus 24

B 6x3−4x2−34x−24
6 x cubed minus 4 x squared minus 34 x minus 24

C 3x3−8x2−7x+12
3 x cubed minus 8 x squared minus 7 x plus 12

D 6x3+20x2−2x−24

Answer 1

The equivalent expression to 2(3x+4)(x−1)(x−3) is 6x³ - 16x² - 14x + 24, obtained through step-by-step polynomial multiplication and simplification. Therefore correct option is A

Step-by-step explanation:

The expression we need to expand and simplify is 2(3x+4)(x−1)(x−3). To find the equivalent expression, we must perform polynomial multiplication. Firstly, we can multiply the two binomials (x−1) and (x−3), then multiply the result by (3x+4), and finally by 2. The steps are:

1. Multiplying the binomials (x−1) and (x−3) results in x² - 4x + 3.
2. Next, we multiply the trinomial x² - 4x + 3 by (3x+4), which gives 3x³ + 4x² - 12x² - 16x + 9x + 12.
3. Simplify to get 3x³ - 8x² - 7x + 12.
4. Finally, multiply by 2 to get 6x³ - 16x² - 14x + 24.

Therefore, the equivalent expression is 6x³ - 16x² - 14x + 24, which corresponds to option A.