Answer: THIRD OPTION.
Step-by-step explanation:
You need to remember that, by definition:
[tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3[/tex]
Given the following expression:
[tex](4k-3b)^3[/tex]
You can identify that:
[tex]a=4k\\b=3b[/tex]
Therefore, you must substitute them into [tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3[/tex] in order to find the equivalent expression for [tex](4k-3b)^3[/tex] in expanded form.
You need to remember the Power of a power property. This states that:
[tex](a^m)^n=a^{mn}[/tex]
Then, you get:
[tex](4k - 3b)^3 = (4k)^3 - 3(4k)^2(3b) + 3(4k)(3b)^2 - (3b)^3=64k^3-144k^2b+108kb^2-27b^3[/tex]
Answer:
The correct option is C) [tex]64k^3-144k^2b+108kb^2-27b^3[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\left(4k-3b\right)^3[/tex]
Apply the perfect cube formula.
[tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]
By using the above formula.
[tex]\left(4k\right)^3-3\left(4k\right)^2\cdot \:3b+3\cdot \:4k\left(3b\right)^2-\left(3b\right)^3[/tex]
[tex]64k^3-144k^2b+108kb^2-27b^3[/tex]
Hence, the correct option is C) [tex]64k^3-144k^2b+108kb^2-27b^3[/tex]
