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Adding and subtracting monomials with different exponents

How to add and subtract monomials with different exponents? How do you add and subtract monomials with different exponents?

Examples of adding and subtracting monomials with different exponents

Example of adding and subtracting monomials with different exponents.

Add and subtract the following monomials with different exponents

8d6 + 6d5d - 5d6

Solution.

8d6 + 6d5d - 5d6 =
8d6 + 6d5d1 - 5d6 =
8d6 + 6d5 + 1 - 5d6 =
8d6 + 6d6 - 5d6 = 9d6

Answer: 9d6.

Example of adding and subtracting monomials with different exponents.

Add and subtract the following monomials with different exponents

26c2d + 4ccd - 5c2d

Solution.

26c2d + 4ccd - 5c2d =
26c2d + 4c1c1d - 5c2d =
26c2d + 4c1 + 1d - 5c2d =
26c2d + 4c2d - 5c2d = 25c2d

Answer: 25c2d.

Example of adding and subtracting monomials with different exponents.

Add and subtract the following monomials with different exponents

7dd + d2 - 6d2

Solution.

7dd + d2 - 6d2 =
7d1d1 + d2 - 6d2 =
7d1 + 1 + d2 - 6d2 =
7d2 + 1d2 - 6d2 =
2d2

Answer: 2d2.

Example of adding and subtracting monomials with different exponents.

Add and subtract the following monomials with different exponents

25y9 - y9 + x9

Solution.

25y9 - y9 + x9 =
25y9 - 1y9 + x9 =
24y9 + x9

Answer: 24y9 + x9.

Note, we can only add like terms (monomials) and we cannot add unlike terms (monomials).