 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that factor out the greatest common monomial factor from this given trinomial and that is 16 a raised to the power 5 b raised to the power 4 minus 48 a b cube plus 24 a cube b square. Let us start with the solution of the given question. Here we are given a trinomial that is 16 a raised to the power 5 b raised to the power 4 minus 48 a b cube plus 24 a cube b square and we have to factor out the greatest common monomial factor. Now we follow the following steps to factor out the greatest common monomial factor and the first step is to find the greatest common number that factors or divides all the given terms in the expression and the greatest common variable factor by choosing the smallest exponent of the variable that occurs in all the terms and then we factor out each term in the expression by the greatest common monomial factor which is the product of the terms obtained in the previous step. Let us first find the greatest common number that factors or divides all the three terms that is 16 48 and 24 in the given expression. Now we see 1 2 4 and 8 are all the common factors of 16 48 and 24 but the greatest common factor is 8. So 8 is the greatest common number that factors or divides 16 48 and 24. Now we find the greatest common variable by choosing the smallest exponent of the variable that occurs in all the terms. Here we have two variables a and b in all the three terms. Now first we see the smallest exponent of variable a that occurs in the three given terms and we see that a raised to power 1 or a is the common variable in all the terms. Similarly b raised to power 2 is the common variable in all the three terms. So the greatest common variable factor is a into b square that is a b square. Now we see that 8 is the greatest common number that factors or divides 16 48 and 24 and a b square is the greatest common variable factor. Thus the greatest common monomial factor is 8 into a b square that is 8 a b square. So now we take 8 a b square common from the three terms or we multiply and divide the given expression by 8 a b square and so we get 8 a b square into 2 a raised to the power 4 b square minus 6 b plus 3 a square the whole. This is the required answer. This completes our session. Hope you enjoyed this session.