Which statements are true? Select each correct answer. 15m3−6m=3m(5m2−6m) 32m4+12m3=4m3(8m+3) 6m2+18m=6m2(1+3m) 40m6−4=4(10m6−1)

Answer:Option (b) and (d) are correct.b) [tex]32m^4+12m^3=4m^3(8m+3)[/tex]d) [tex]40m^6-4=4(10m^6-1)[/tex]Step-by-step explanation:Given: Some statement We have to check which statements are true.We will check all one by one.Consider a) [tex]15m^3-6m=3m(5m^2-6m)[/tex]Consider the Left hand side of the given statement, [tex]15m^3-6m[/tex]Taking 3m common from each term, we have, [tex]15m^3-6m=3m(5m^2-2m)[/tex]Thus, LHS ≠ RHSThus, the statement is false.b) [tex]32m^4+12m^3=4m^3(8m+3)[/tex]Consider the Left hand side of the given statement, [tex]32m^4+12m^3[/tex]Taking [tex]4m^3[/tex] common from each term, we have,[tex]32m^4+12m^3=4m^3(8m+3)[/tex]Thus, LHS = RHSThus, the statement is True.c) [tex]6m^2+18m=6m^2(1+3m)[/tex]Consider the Left hand side of the given statement, [tex]6m^2+18m[/tex]Taking 6m common from each term, we have,[tex]6m^2+18m=6m(m+3)[/tex]Thus, LHS ≠ RHSThus, the statement is false.d) [tex]40m^6-4=4(10m^6-1)[/tex]Consider the Left hand side of the given statement, [tex]40m^6-4[/tex]Taking 4 common from each term, we have,[tex]40m^6-4=4(10m^6-1)[/tex]Thus, LHS = RHSThus, the statement is True.Thus, Option (b) and (d) are correct.