Answer :
[tex](4x - 3)(3 {x}^{2} - 4x - 3)[/tex]
We can use a Punnett Square to FOIL this (picture attached).
From this, we find that is equals
[tex]12 {x}^{3} - 16 {x}^{2} - 12x \\ - 9 {x}^{2} + 12x + 9[/tex]
We can simplify this to equal
[tex]12 {x}^{3} - 25 {x}^{2} + 9[/tex]
This is answer D.
Final answer:
The correct simplification of (4x - 3)(3x^2 - 4x - 3) is 12x^3 - 25x^2 + 9, which is option D.
Explanation:
The correct simplification of the expression (4x - 3)(3x^2 - 4x - 3) is found by using the distributive property to multiply each term in the first polynomial by each term in the second polynomial. The process is as follows:
- Multiply 4x by each term in the second polynomial: 4x × 3x^2 = 12x^3, 4x × (-4x) = -16x^2, 4x × (-3) = -12x.
- Multiply -3 by each term in the second polynomial: -3 × 3x^2 = -9x^2, -3 × (-4x) = 12x, -3 × (-3) = 9.
- Combine like terms from the above products: 12x^3 + (-16x^2 - 9x^2) + (-12x + 12x) + 9.
- Simplify the combined terms: 12x^3 + (-25x^2) + 9.
The final simplified expression is 12x^3 - 25x^2 + 9, which corresponds to option D.
