Factor each polynomial. See Examples 5 and 6.

Question

36 z^{2} - 81 y^{4}

Accepted Answer

Hey, everyone here we are asked to completely factor the following difference of squares expression where we have 64 M squared minus 225 and to the fourth power. Now, the first thing we can notice with this expression here is that the coefficients are perfect squares and the exponents of their variables are even numbers. So we can use the difference of squares formula. But before we do that, we want to rewrite these terms as their squares. So we can see with 64 M squared, this is equivalent to eight M, the quantity of eight M squared. And then for our second term, we have 225 and to the fourth power. Well, this is equivalent to the quantity of 15 and squared raised to the second power. So now with our original terms written as squares, we can go ahead and use the difference of squares formula, which if we recall this formula is X squared minus Y squared is equal to the quantity of X plus Y times the quantity of X minus Y. And now we just have to compare this formula with our rewritten expression to identify our values for X and Y. So beginning with our value for X, what we see from the formula that X squared is going to be our first term. So we can see that X squared is going to be this quantity of A M squared, which tells us that our value for X is just eight M. And now moving on to the value for Y when we see why squared is going to be our second term from our expression. So we see that Y squared is the quantity of 15 and squared raised to the second power which tells us here that our value for just why is just going to be 15 and squared. So now that we have our X and Y values identified, we can go ahead and use our formula here to find the factored form of our original expression. So again, our original expression here, we have 64 M squared minus 225 and to the fourth power. And from our formula, we see that this expression, this difference of squares expression is equivalent to the quantity of eight M plus 15 And squared times the quantity of AM -15 and squared. So with this, we have found our fully factored form of our original expression and therefore we are left with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor each polynomial. See Examples 5 and 6. $36 z^{2} - 81 y^{4}$

Key Concepts

Difference of Squares

Greatest Common Factor (GCF)

Factoring Polynomials

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