Video: Subtraction of Two Algebraic Expressions

Find 𝐴 − 𝐵 given that 𝐴 = 3𝑞² + 5 and 𝐵 = 2𝑞² + 6.

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Video Transcript

Find 𝐴 minus 𝐵 given that 𝐴 is equal to three 𝑞 squared plus five and 𝐵 is equal to two 𝑞 squared plus six.

We are asked to find 𝐴 minus 𝐵. This means that we need to subtract expression 𝐵 from expression 𝐴. One way of doing this is to line up the like terms. We have three 𝑞 squared and two 𝑞 squared and we have positive five and positive six. We need to subtract the bottom line from the top line. Three 𝑞 squared minus two 𝑞 squared is equal to one 𝑞 squared. We write this as 𝑞 squared. It is important to note here that the exponents or power — the squared in this case — does not change when adding or subtracting.

When dealing with the constants, we have positive five minus positive six. Subtracting a positive number is the same as taking away or subtracting the number itself. We have positive five minus six. This is equal to negative one as six places below five on a number line is negative one.

If 𝐴 is equal to three 𝑞 squared plus five and 𝐵 is equal to two 𝑞 squared plus six, then 𝐴 minus 𝐵 is equal to 𝑞 squared minus one.

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