Question

factor the algebraic expression. 64m^5 - 16m^3 = 16m^3(_m - - _) 64m^5 - 16m^3 = 16m^3(□m^□ - □)

Explanation:

Step1: Factor out the common factor

First, factor out the greatest - common factor \(16m^{3}\) from \(64m^{5}-16m^{3}\). We get \(16m^{3}(4m^{2} - 1)\).

Step2: Recognize the difference - of - squares

The expression \(4m^{2}-1\) is a difference of squares, since \(4m^{2}=(2m)^{2}\) and \(1 = 1^{2}\). The formula for factoring a difference of squares \(a^{2}-b^{2}=(a + b)(a - b)\), here \(a = 2m\) and \(b = 1\), so \(4m^{2}-1=(2m + 1)(2m-1)\).

Answer:

\(64m^{5}-16m^{3}=16m^{3}(4m^{2}-1)=16m^{3}(2m + 1)(2m - 1)\)