Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6)...

Question

Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)

Accepted Answer

Hello, everyone. We are given a polynomial expression and asked to perform the indicated operations to simplify it. The expression we are given is three multiplied by open parentheses. 10 H squared plus seven H minus three closed parentheses minus five, multiplied by open parentheses. 4h squared minus six H plus nine closed parentheses. Our answer choices are a 10 H squared plus 51 H minus 54 B H squared minus nine H plus C 10 H squared minus nine H minus 54 D 50 H squared plus 51 H minus 54. I'm gonna begin by rewriting our ex expression. So three multiplied by the parentheses. 10, each squared plus seven minus three closed parentheses minus five, multiplied by open parentheses. 4h squared minus six H plus nine, closed parentheses. Before I can combine any like terms, I need to distribute the values outside the parentheses into the parentheses. So I'm gonna multiply three by 10 squared and get 30 squared. Then three multiplied by seven H is plus H and then three multiplied by negative three is negative nine. Next, I'm gonna distribute negative five into the second set. Of parentheses. I'm taking the minus sign with my five. So that way it doesn't get lost. So I'm gonna treat it as a negative five. Negative five multiplied by 4h squared is negative 20 H squared, negative five, multiplied by negative six H is positive 30 H and negative five multiplied by positive nine is negative 45. So at this step, we have 30 H squared plus 21 H minus nine minus 20 H squared plus 30 H minus 45. Now, we need to combine our like terms. We're gonna start with the highest exponent and make sure we take the sign in front of the term with us. So we'll start with H squared. We have 30 squared and negative 20 each squared which will combine to a positive 10 squared. Next looking for my single age term, I have positive 21 inch and a positive 30 which will combine to a positive and then our constants, we have negative nine and negative 45 which will combine to negative 54. So there are no more like terms. So this is as simplified as it gets, we have 10 H squared plus 51 H minus 54. And that's answer choice. A have a nice day.

Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)

Key Concepts

Distributive Property

Combining Like Terms

Polynomial Subtraction

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