Video: Subtraction of Two Algebraic Expressions

Find 𝐴 βˆ’ 𝐡, given 𝐴 = 5π‘₯Β³ βˆ’ 3π‘₯ and 𝐡 = βˆ’6π‘₯Β² + 3π‘₯.

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Video Transcript

Find 𝐴 minus 𝐡, given 𝐴 is equal to five π‘₯ cubed minus three π‘₯ and 𝐡 is equal to negative six π‘₯ squared plus three π‘₯.

In order to answer this question, we need to subtract negative six π‘₯ squared plus three π‘₯ from five π‘₯ cubed minus three π‘₯. Before we start, it’s important to remember that we can only collect or group terms with the same exponent or power.

In this case, the only terms we can group together are negative three π‘₯ and positive three π‘₯. We also need to remember our rules when two signs are touching. If we have two positive signs, the resultant sign is a positive one or an addition sign. When we have a positive and a negative sign, in either order, our resultant sign is a negative or subtraction sign. And when we have two negative signs, the resultant sign is positive or addition.

The only term with π‘₯ cubed in it is the first one, five π‘₯ cubed. So this too must be in our answer. We have a negative six π‘₯ squared term. However, this term is being subtracted. In other words, we have negative negative six π‘₯ squared. Two negatives become a positive. Therefore, this is the same as six π‘₯ squared or positive six π‘₯ squared.

Finally, we need to group the π‘₯ terms, negative three π‘₯ minus positive three π‘₯. This time, our sign will become a subtraction or negative sign. So we’re left with negative three π‘₯ minus three π‘₯. Negative three minus three is equal to negative six. Therefore, negative three π‘₯ minus three π‘₯ equals negative six π‘₯.

This means that if 𝐴 is equal to five π‘₯ cubed minus three π‘₯ and 𝐡 is equal to negative six π‘₯ squared plus three π‘₯, then 𝐴 minus 𝐡 equals five π‘₯ cubed plus six π‘₯ squared minus six π‘₯.

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