Work out the value of three times three 𝑎 minus 𝑏 when 𝑎 equals four and 𝑏 equals 17.
To solve this expression, we’ll need to consider our order of operations: brackets, indices, multiplication and division, followed by addition and subtraction. We know that 𝑎 equals four and 𝑏 equals 17. So we need to substitute these values in for 𝑎 and 𝑏 in the expression. And now our expression looks something like this: three times three times four minus 17. Following our order of operations, we first need to solve what is in the brackets. And inside the brackets, we’ll also follow the order of operations.
We don’t have any indices. But we do have multiplication. Three times four equals 12. And then, we bring everything else down. We still need to calculate inside the brackets. But there’s only subtraction left. 12 minus 17 equals negative five. Bring down the three. And our final step will be multiplying three times negative five which is negative 15. Let’s consider one other way of solving this problem.
Three times three 𝑎 minus 𝑏 can be expanded and rewritten. Since we’re multiplying three by everything in the brackets, we could multiply three times three 𝑎. We multiply three by the coefficient three and then keep the variable 𝑎. Three times three 𝑎 equals nine 𝑎. Now, we need to multiply three by 𝑏. Be careful with your sign here. Make sure you bring down that subtraction. 𝑏 had a coefficient of one. So we’re multiplying three times one which equals three 𝑏. Again, make sure you bring down your subtraction. Three times three 𝑎 minus 𝑏 is the same thing as nine 𝑎 minus three 𝑏.
And at this point, we’ll need to substitute in our values for 𝑎 and 𝑏. And we’ll have nine times four minus three times 17. Nine times four is 36. Three times 17 is 51. 36 minus 51 equals negative 15.