The following is a proof of the algebraic equivalency of (2x)³ and 8x³. Fill in each of the blanks with either the statement commutative property or associative property.(2x)³ =2x∙2x∙2x =2(x×2)(x×2)x ___________________ =2(2x)(2x)x ___________________ =2∙2(x×2)x∙x ___________________ =2∙2(2x)x∙x ___________________ =(2∙2∙2)(x∙x∙x) ___________________ =8x³

You're using the commutative property when you swap the order of factors in a multiplication:[tex]a\cdot b = b\cdot a[/tex]and you use the associative property when you regroup the products of more than 2 factors in a different way:[tex](a\cdot b)\cdot c = a\cdot (b\cdot c)[/tex]So, you're constantly alternating between associative and commutative. Try to see which property you're using in the first step, and then keep alternating between the two!