Find each product. See Example 5.

(q - 2)⁴

Question

Find each product. See Example 5.

(q - 2)⁴

Accepted Answer

Hey, everyone here, we are asked to perform the indicated operations to simplify the given expression where we have the quantity of H minus five. Raise to the fourth power. Here we have four answer choice options. Answer choice. A raise to the fourth power minus 625. Answer bh raise to the fourth power minus 25 H squared plus 625. Answer ch raises to the fourth power minus five HQ plus 25 H squared minus 625 and answer DH raise to the fourth power minus H cubed plus 150 H squared minus 500 H plus 625. So to begin simplifying our given expression, we first want to recall the formula where we have the quantity of X minus Y raised to the fourth power is equivalent to the expression X raise to the fourth power minus four X qed multiplied by Y plus six X squared, multiplied by Y squared minus four X multiplied by YQ plus Y raised to the fourth power. So to begin now applying this formula, we just want to compare the left side of this formula with our given expression to identify our values for X and Y. So starting with X, we see from our given expression that X is going to be H and that means Y is going to be five. So now we just want to start finding our terms on the right side of our formula. So we can begin with X raised to the fourth power. Well, again, X is just H so X raised to the fourth power is just H raised to the fourth power. We then have X cubed, X cubed gives us H cubed. Then we have X squared, X squared is just H squared. And then now we can move on to our Y terms. So we have Y is five and now we have Y squared which gives us five squared and five squared simplifies 2 25. We then have Y cubed which gives us five cubed and five cube simplifies to 125. And then we have Y ra raised to the fourth power which gives us five, raised to the fourth power. And this value simplifies to 625. And so now we can start substituting in our X and Y values into the right side of our formula. So so far, we have the quantity of H minus five raised to the fourth power is equivalent two X raise to the fourth power which we identified as H raise to the fourth power, we then have minus four multiplied by H cubed multiplied by five. We then have plus six multiplied by H squared, multiplied by 25. Then we have minus four multiplied by H multiplied by 125. And lastly, we have plus 625. Now, our last step in simplifying our expression is to just perform the necessary multiplication. And so in doing this, we have H raised to the fourth power minus 20 HQ plus 125 or multiplied by H squared. Then we have minus 500 H and plus 625. So after multiplying, we see that we are left with our simplified expression. And so we have answer choice D where we are left with H raises to the fourth power minus H cubed plus 150 H squared minus 500 H plus 625. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find each product. See Example 5. (q - 2)⁴

Key Concepts

Polynomial Expansion

Binomial Theorem

Coefficients and Exponents

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