To determine which option is not a correct way to rewrite the expression [tex]\((4x^2 + 3x - 7)(x - 2)\)[/tex] using the distributive property, let's analyze each option in detail.
### Option A:
[tex]\[
(4x^2 + 3x - 7)(x) + (4x^2 + 3x - 7)(-2)
\][/tex]
This option distributes the expression [tex]\((4x^2 + 3x - 7)\)[/tex] over both [tex]\(x\)[/tex] and [tex]\(-2\)[/tex]. This is a correct use of the distributive property.
### Option B:
[tex]\[
(4x^2)(x) + (4x^2)(-2) + (3x)(x) + (3x)(-2) + (-7)(x) + (-7)(-2)
\][/tex]
This option breaks the original expression down into separate terms and distributes each term individually over [tex]\(x\)[/tex] and [tex]\(-2\)[/tex]. This is also a correct application of the distributive property.
### Option C:
[tex]\[
(4x^2)(x - 2) + (3x)(x - 2) + (-7)(x - 2)
\][/tex]
This option groups the original expression into three parts [tex]\((4x^2)\)[/tex], [tex]\((3x)\)[/tex], and [tex]\((-7)\)[/tex], and then distributes each part over [tex]\((x - 2)\)[/tex]. This is another correct use of the distributive property.
### Option D:
[tex]\[
(4x^2 + 3x - 7)(x) + (4x^2 + 3x - 7)(x - 2)
\][/tex]
In this option, the original expression [tex]\((4x^2 + 3x - 7)\)[/tex] is distributed over both [tex]\(x\)[/tex] and [tex]\((x - 2)\)[/tex] separately. However, when we combine these into a single expression, it does not align correctly with the distributive property because it does not factor out the common [tex]\((x - 2)\)[/tex] term properly.
Therefore, the incorrect option is:
[tex]\[
\boxed{D}
\][/tex]
