Question Video: Subtracting Two Algebraic Expressions

Video Transcript

Find 𝐴 minus 𝐵 given that 𝐴 equals eight 𝑥 plus two and 𝐵 equals five 𝑥 minus one.

If we want to solve 𝐴 minus 𝐵, we plug in eight 𝑥 squared plus two for 𝐴 and five 𝑥 minus one for 𝐵. When we’re working with subtraction of terms, the parentheses are very important. This is because we are subtracting all of 𝐵 from 𝐴. And to do that, we have to distribute this subtraction across both terms for the expression in 𝐵. And that means we’re saying eight 𝑥 plus two minus five 𝑥 but plus one because we’re subtracting a negative one. And that means we’re adding. This is the step where if you’re not careful, you will get a sign mistake.

And so when you’re subtracting expressions, you need to be very careful to distribute the subtraction correctly. Once you do that, it’s a simple matter of combining like terms. We have two terms with an 𝑥-variable and two whole numbers. For our 𝑥-variable, we have eight 𝑥 minus five 𝑥. And that means we’ll subtract five from eight. Remember, the variable doesn’t change. We just do the subtraction from the coefficients. And then we have two plus one, which is three. Eight minus five is three. So we have three 𝑥 plus three. In this case, under these conditions, 𝐴 minus 𝐵 is equal to three 𝑥 plus three.