High School

Find the product of [tex](4x^3 + 2x^2)(6x - 9)[/tex]. Provide your answer in descending order of exponents.

A. [tex]48x^5[/tex]
B. [tex]48x^6[/tex]
C. [tex]48x^7[/tex]
D. [tex]48x^8[/tex]

Answer :

Final answer:

The product of [tex](4x^3 - 2x^2)(6x - 9)[/tex] is [tex]24x^4 - 12x^3 + 18x^2.[/tex]

Explanation:

To find the product of [tex](4x^3 - 2x^2)(6x - 9)[/tex], we can use the distributive property.

Multiplying the first terms, we get [tex]4x^3 * 6x = 24x^4[/tex]

Multiplying the outer terms, we get [tex]4x^3 * -9 = -36x^3[/tex]

Multiplying the inner terms, we get [tex]-2x^2 * 6x = -12x^3.[/tex]

Multiplying the last terms, we get [tex]-2x^2 * -9 = 18x^2.[/tex]

Combining the like terms, we have [tex]24x^4 - 12x^3 + 18x^2.[/tex]

Therefore, the product of [tex](4x^3 - 2x^2)(6x - 9)[/tex] is [tex]24x^4 - 12x^3 + 18x^2.[/tex]