the distributive property can be applied to which expression to factor (12x^{3}-9x^{2}+4x…

the distributive property can be applied to which expression to factor (12x^{3}-9x^{2}+4x - 3)?\n(3(4x^{3}-1)-(9x^{2}+4x))\n(4x(3x^{2}+1)-3(3x^{2}-1))\n(3x(4x - 3)-(3 + 4x))\n(3x^{2}(4x - 3)+1(4x - 3))

the distributive property can be applied to which expression to factor (12x^{3}-9x^{2}+4x - 3)?\n(3(4x^{3}-1)-(9x^{2}+4x))\n(4x(3x^{2}+1)-3(3x^{2}-1))\n(3x(4x - 3)-(3 + 4x))\n(3x^{2}(4x - 3)+1(4x - 3))

Answer

Explanation:

Step1: Expand each option

  • Option 1: $$3(4x^{3}-1)-(9x^{2}+4x)=12x^{3}-3 - 9x^{2}-4x\neq12x^{3}-9x^{2}+4x - 3$$
  • Option 2: $$4x(3x^{2}+1)-3(3x^{2}-1)=12x^{3}+4x-9x^{2}+3\neq12x^{3}-9x^{2}+4x - 3$$
  • Option 3: $$3x(4x - 3)-(3 + 4x)=12x^{2}-9x-3 - 4x=12x^{2}-13x-3\neq12x^{3}-9x^{2}+4x - 3$$
  • Option 4: $$3x^{2}(4x - 3)+1(4x - 3)=(3x^{2}+1)(4x - 3)=12x^{3}-9x^{2}+4x - 3$$

Answer:

$3x^{2}(4x - 3)+1(4x - 3)$ (the fourth option)