Q:

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)

Accepted Solution

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