Which expression is equivalent to (4k−3b)3 in expanded form?64k3−144kb2+108k2b−27b364k3−48k2b+36kb2−27b364k3−144k2b+108kb2−27b364k3−48kb2+36k2b−27b3

Accepted Solution

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]