Factor each polynomial. See Examples 5 and 6. y^4-81

Question

Accepted Answer

Hey, everyone here, we are asked to completely factor the following difference of squares expression where we have Q squared minus 49. Now our first step here in factoring this expression is to recall the difference of squares formula which tells us that X squared minus Y squared is equivalent to the quantity of X plus Y times the quantity of X minus Y. And now all we have to do is compare our formula here with our expression to identify the values for X and Y. So beginning with our value for X, while looking at the formula, we see that X squared is going to be the first term from our expression. So we see that X squared is just Q squared which tells us that X alone is just going to be Q. And now finding our value for Y from the formula, we see that Y squared is going to be the second term from our expression. So Y squared is equal to 49 which tells us that Y is going to be seven. So now with our values for X and Y clearly identified, we can go ahead and just use our formula here to find the factored form of our original expression. So again, our original expression, we have Q squared minus 49. And from our formula, we know that this expression is equivalent to the quantity of Q plus seven times the quantity of Q minus seven. And with this, we have found our fully factored form of our original expression. And therefore, we are left with answer choice B thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Factor each polynomial. See Examples 5 and 6. y^4-81

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