Which expression is equivalent to three 𝑎 minus four 𝑎 multiplied by 11𝑎 minus 𝑎. Circle your answer. The options are: negative 11𝑎 squared minus 𝑎, negative 10𝑎 squared, two 𝑎 minus 44𝑎 squared, or three 𝑎 minus 40𝑎 squared.
So to solve this problem and simplify the expression, what we need to use is BIDMAS. And what BIDMAS is, is a tool to help us remember which order to do our operations in. So we have brackets, indices, division, multiplication, addition, and subtraction. Well, we can see that in our expression, we have subtraction and multiplication. And if we check BIDMAS, we can see that the multiplication comes first. So therefore, we’re gonna use this first to simplify our expression.
So, for our expression, we’re gonna do the four 𝑎 multiplied by 11𝑎 first. So I, actually, just put it in brackets so we can see that we’re gonna do that first. So we’re gonna have three 𝑎 minus. And then when we multiply two terms, we multiply the coefficients first. So we have four by 11 which gives us 44. And then we have 𝑎 multiplied by 𝑎 which gives us 𝑎 squared. So we’ve got 44𝑎 squared. And then, finally, we’ve got minus 𝑎.
So the next thing we need to do is simplify or collect any like terms. But we’ve got three 𝑎 and negative 𝑎. These are the only like terms because we can remember that we can’t add or subtract any terms that have a different pair of 𝑎, in this case. So we couldn’t add or subtract 𝑎 squareds away from 𝑎s. So then if we do three 𝑎 minus 𝑎, we get two 𝑎. Then we’ve got minus 44𝑎 squared. So, therefore, we can say that the expression equivalent to three 𝑎 minus four 𝑎 multiplied by 11𝑎 minus 𝑎 is two 𝑎 minus 44𝑎 squared.