Question Video: Subtracting Two Algebraic Expressions | Nagwa Question Video: Subtracting Two Algebraic Expressions | Nagwa

Question Video: Subtracting Two Algebraic Expressions Mathematics • First Year of Preparatory School

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Find ๐ด โˆ’ ๐ต given ๐ด = 8๐‘ฅ + 2 and ๐ต = 5๐‘ฅ โˆ’ 1.

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Video Transcript

Find ๐ด minus ๐ต given that ๐ด equals eight ๐‘ฅ plus two and ๐ต equals five ๐‘ฅ minus one.

If we want to solve ๐ด minus ๐ต, we plug in eight ๐‘ฅ squared plus two for ๐ด and five ๐‘ฅ minus one for ๐ต. When weโ€™re working with subtraction of terms, the parentheses are very important. This is because we are subtracting all of ๐ต from ๐ด. And to do that, we have to distribute this subtraction across both terms for the expression in ๐ต. And that means weโ€™re saying eight ๐‘ฅ plus two minus five ๐‘ฅ but plus one because weโ€™re subtracting a negative one. And that means weโ€™re adding. This is the step where if youโ€™re not careful, you will get a sign mistake.

And so when youโ€™re subtracting expressions, you need to be very careful to distribute the subtraction correctly. Once you do that, itโ€™s a simple matter of combining like terms. We have two terms with an ๐‘ฅ-variable and two whole numbers. For our ๐‘ฅ-variable, we have eight ๐‘ฅ minus five ๐‘ฅ. And that means weโ€™ll subtract five from eight. Remember, the variable doesnโ€™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 ๐‘ฅ plus three. In this case, under these conditions, ๐ด minus ๐ต is equal to three ๐‘ฅ plus three.

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