Factor each polynomial. See Examples 5 and 6. 25s^4-9t^2

Question

Accepted Answer

Hey, everyone here, we are asked to completely factor the following difference of squares expression where we have 169 k to the fourth power minus 81 P squared. Now, the first thing we need to notice here with this expression is that our coefficients for both of the terms here are perfect squares and the exponents for each variable are even numbers. So we can go ahead and begin by rewriting our original expression by rewriting each term as third square. So beginning with our first term of 169 K to the fourth power. Well, this is equivalent to the quantity of 13 K squared raised to the second power. And with our second term here of 81 P squared. Well, this is equivalent to the quantity of nine P raised to the second power. So now looking at our rewritten expression, we can see that we clearly have the difference of two squares. Therefore, we can recall the difference of squares formula which tells us that X squared minus Y squared is equal to the quantity of X plus Y times the quantity of X minus Y. And now our next step is to just compare our formula here with our rewritten expression. So we can find our values for X and Y. So beginning with our value for X. Well, we can see from the formula that X squared is going to be our first term from our expression here. So we see squared is the quantity of 13 k squared raised to the second power. And this tells us that just X alone is going to be 13 k squared. And now finding our value for why? While looking at the formula, we see that Y squared is going to be the second term from our expression. Therefore, why squared is the quantity of nine P squared? And this tells us that Y is just going to be nine P. And now with the values for X and Y clearly identified, we can go ahead and use our formula to find the factored form of our original expression. So again, our original expression here, we have 169 K to the fourth power minus 81 P squared. And from our formula, we see that this expression is equivalent to the factored form where we have the quantity of 13 k squared plus nine P times the quantity of 13 k squared minus nine P. And with this, we have found our fully factored form of our original expression. 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.

Factor each polynomial. See Examples 5 and 6. 25s^4-9t^2

Key Concepts

Factoring Polynomials

Difference of Squares

Exponents and Polynomial Terms

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