Evaluate 𝑧 squared plus four 𝑦 minus one, given that 𝑦 equals two and 𝑧 equals four.
So, to solve this problem, what we need to do is substitute 𝑦 equals two and 𝑧 equals four into our expression. But before we can do that, we need to see what each term means. So, first of all, we have 𝑧 squared. And what does 𝑧 squared actually mean? Well, 𝑧 squared means 𝑧 multiplied by 𝑧. And four 𝑦 means four multiplied by 𝑦. So, we can say that four 𝑦 equal to four multiplied by 𝑦. Okay, great! Now we know what our terms mean. So, let’s get on and solve the problem.
So, now when we substitute in 𝑦 equals two and 𝑧 equals four, we get four squared, that’s because 𝑧 is equal to four, so we get four squared, plus four multiplied by two, and that’s because we had four multiplied by 𝑦, and 𝑦 is equal to two, then minus one.
So, to help us, what we’re gonna use is something called PEMDAS. Because this tells us our order of operations. So, first of all we have parentheses. Then we have exponents. Then next is multiplication. Then next is division, followed by addition. And then finally, we have subtraction. So, taking a look at PEMDAS, we can see that we’re gonna do parentheses first.
So, we’ll take a look at our parentheses. And inside our parentheses, we have four multiplied by two. So, we’re gonna get four squared plus eight minus one. And we get that because four multiplied by two is eight. So, that’s our parentheses dealt with. So, now we can move on to exponents.
Well, we got four squared. So, that’s our exponent. So, we get 16 add eight minus one. And that’s our exponents now dealt with. Well, then, we have multiplication and division. But we don’t have any multiplication or division to do at this point. So, we can move on from those. So then, we complete our addition.
We have 24 minus one. And that’s because 16 add eight is 24. And then, finally, we carry out the subtraction. So, 24 minus one gives us 23. It’s worth saying at this point that the addition and subtraction could’ve been done either way round. It wouldn’t have affected the final answer. So, we can say that we we’ve evaluated 𝑧 squared plus four 𝑦 minus one, given that 𝑦 equals two and 𝑧 equals four. And when we’ve done that, the result is 23.