Find 𝐴 minus 𝐵, given that 𝐴 is equal to seven 𝑝 squared minus four 𝑝 plus five and 𝐵 is equal to three 𝑝 squared minus four 𝑝 plus one.
In order to answer this question, we need to subtract three 𝑝 squared minus four 𝑝 plus one from seven 𝑝 squared minus four 𝑝 plus five.
Before we start this question, it’s important to remember our rules when two signs are touching. If we have two positive signs, our resultant sign will also be positive or an addition sign. If the signs are different, a positive and a negative, then the resultant sign will be a negative or subtraction sign. And if both signs are negative, the resultant sign will be positive.
It is also really important to remember that we can only group or collect the terms with the same exponents or powers. Firstly, we can group seven 𝑝 squared and three 𝑝 squared. Seven 𝑝 squared minus three 𝑝 squared is equal to four 𝑝 squared as seven minus three equals four. Next, we can group the 𝑝 terms, negative four 𝑝 minus negative four 𝑝. The two negatives become a positive. So we have negative four 𝑝 plus four 𝑝. This is equal to zero 𝑝 or zero. So there will be no 𝑝 term in the answer.
Finally, we need to group the numbers, positive five and positive one. Here we have positive five minus positive one. The negative and positive signs turn into a negative. So we are left with positive five minus one. This is equal to four or positive four.
This means that if 𝐴 is equal to seven 𝑝 squared minus four 𝑝 plus five and 𝐵 is equal to three 𝑝 squared minus four 𝑝 plus one, then 𝐴 minus 𝐵 is equal to four 𝑝 squared plus four.