Lesson 1 · from §20 of the 1910 text
Subtracting Monomials
Subtraction of monomials works exactly like subtraction of signed numbers in Chapter 2.
Rule. Change the sign of the subtrahend, then find the algebraic sum of the result and the minuend.
- From +8a take +3a: \;8a - 3a = 5a.
- From 6ax take -4ax: \;6ax + 4ax = 10ax.
- Subtract 7a^2b from -10a^2b: \;-10a^2b - 7a^2b = -17a^2b.
- Subtract -9xy^2 from 3xy^2: \;3xy^2 + 9xy^2 = 12xy^2.
Quick check
From -4m^2 take -9m^2.
The difference of two dissimilar monomials can't be one term, so it's written as a binomial:
- Subtract +a from +b: \;b - a.
- Subtract -5b from 3c: \;3c + 5b.
- Subtract 4xy from -3x^2z: \;-3x^2z - 4xy.
Try to change the sign of the subtrahend in your head as soon as you can.
Quick check
Subtract 6y from -2x.
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
For each pair, subtract both ways.
Subtract the first monomial from the second, and the second from the first: 2 x and 3 x.
Subtract the first monomial from the second, and the second from the first: 4 x and 3 x.
Subtract the first monomial from the second, and the second from the first: - 2 x and - 3 x.
Subtract the first monomial from the second, and the second from the first: - 5 x and - 3 x.
Subtract the first monomial from the second, and the second from the first: - x and 4 x.
Subtract the first monomial from the second, and the second from the first: - x and - 3 x.
Subtract the first monomial from the second, and the second from the first: - c and 5 c.
Subtract the first monomial from the second, and the second from the first: - a c and - 5 a c.
Subtract the first monomial from the second, and the second from the first: 8 a^{2} c and - 11 a^{2} c.
Subtract the first monomial from the second, and the second from the first: 6 x^{2} y^{2} and - 6 x^{2} y^{2}.
Subtract the first monomial from the second, and the second from the first: 3 x and 0.
Subtract the first monomial from the second, and the second from the first: - 4 a b and 0.
Subtract the first monomial from the second, and the second from the first: a and b.
Subtract the first monomial from the second, and the second from the first: c and 2 x.
Subtract the first monomial from the second, and the second from the first: x and - 4 y.
Subtract the first monomial from the second, and the second from the first: - 3 a and 2 b.
Subtract the first monomial from the second, and the second from the first: - 2 a and - 5 b.
Subtract the first monomial from the second, and the second from the first: - 2 a and - 2 a.