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.