In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(...

Question

In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(7y+2)

Accepted Answer

Welcome back. I'm so glad you're here. We've got an expression and we get to simplify it. Let me rewrite this. It's 12 Y plus two times parentheses to minus six Y. And parentheses. And so how do we know how to simplify this? We recall from previous lessons that we have the acronym penned us which tells us the order of operations to do We start with parentheses for P. And we look and do we have any parentheses? Yes we do. We've got parentheses with the two minus six Y. And inside the parentheses is the operation subtraction. Now there's one caveat for addition and subtraction. We can only add and subtract like terms and two and minus six Y. Are not like terms. So we can't do that subtraction. Now we can look at the parentheses and say do they serve another function? Do they have a number squished up against them in front of them? That indicates multiplication. And we would multiply and distribute that. Yes. This too squished up in front tells us we have to take the two times the two and times the negative six Y. So we've got multiplication operation and in front of that we've got an addition operation. So which one do we do first? Well we don't have to do any operations inside of parentheses. We can't we don't have exponents and next is multiple multiplication and division from left to right. And so we start with multiplication before addition. So we take that two and multiply it by the two inside the parentheses. And that'll give us four. We take the two times the negative six Y. Inside the parentheses because that will give us negative 12 Y. And it's okay to multiply and divide things that aren't like terms. We just can't add or subtract. Now let's bring down the rest of it which is just 12 Y. Plus. And now all we've got going on our addition and subtraction. So we're done with multiplication and division and we can add and subtract like terms. So what here are like terms? Well 12 Y and minus 12 Y. Well we've got 12 Y minus 12 Y. That's just going to equal zero. So I'm not going to write that on the next line. I'm just going to bring down what's left which is four. We look at our answer choices and that matches with answer choice. A well done we'll catch you on the next one.

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