Algebra of Educational applications

3. Similar terms
to print

Name: ______________________________________ Subject: _______________________ Date: _______

Write on the right side what is missing.

1. Similar terms

Two terms are similar when they have the same literal and the same exponent.

Example: 6a² y -7a² are similar.

-4xy, 3xy y -2xy are similar.

8a²b³ y -7a²b³ are similar.

4n³x² y -2x2n3 are similar, although the letters are not in the same order.

8a³ y 4a² are not similar because their exponents are not the same.

-9n⁵ y 5m⁵ are not similar because their literal part is not the same.

7a²b³ y 2a²b² are not similar because the exponent in b is not the same

5n²y⁵ y 9y²n⁵ are not similar because their exponents are not the same.

A. Choose the correct answer: a, b, c.

1. Are the terms 5a³b and -8a³b similar?
a. SI b. NO
2. Are the terms -a²b² and 5a³b similar?
a. SI b. NO
3. Are the terms 5m²x², -7mx³ and 5m³x similar?
a. SI b. NO
4. Are the terms -m⁴, 7m⁴ and -3m⁴ similar?
a. SI b. NO
5. Los términos 5mx³ and -7x³m similar?
a. SI b. NO
6. Are the terms 2ay² and 4ya² similar?
a. SI b. NO

2. Laws of the signs

The laws of the signs for multiplication and division are different from the laws for addition and subtraction.

For multiplication and division the laws are as following: plus by plus is plus; minus by minus is plus; plus by minus is minus and minus by plus is minus.

The laws of the sign for addition and subtraction are as following:

1. If the signs are the same we must sum and repeat the sign.

Ejemplos: + 2 + 7 = +9; -6 -4 = -10

2. When the signs are opposite, we subtract and write the sign of the higher number.

Example: +7 -4 = +3 ; -9 +2 = -7

B. Choose the correct answer: a, b or c.

1. In multiplication and division: minus multiplied by plus is
a. Plus b. Minus
2. In multiplication and division: minus multiplied by minus is
a. Plus b. Minus
3. In addition and subtraction, if the signs are the same we repeat the sign: plus and plus has as a result:
a. Plus b. Minus
4. In addition and subtraction, if the signs are the same we repeat the sign: minus and minus has as a result
a. Plus b. Minus
5. What is the result of +9 and -2 ?
a. 11 b. -7 c. 7
6. What is the result of -12 and 4 ?
a. -12 b. -8 c. 8

3. Reducing similar terms

The terms of the following polynomial are similar: 4x +3x because its literal part and its exponent are equals.

-4x -12x are similar.

If the terms are similar, we repeat the literal part and sum the coefficient and we sum the coefficient, observing the laws of the sign.

4x +3x = 7x

-4x -12x = -16x

C. Choose the correct answer: a, b or c.

1. Reduce these similar terms: -7x + 2x
a. -5x b. -9x c. 5x
2. Reduce: 8y - 3y
a. 11y b. -5y c. 5y
3. Reduce: 9ay + 7ay
a. 2ay b. 16ay c. -2ay
4. Reduce: -5mx - 4mx
a. 9mx b. -mx c. -9mx
5. Reduce: -12xy + 7xy
a. -5xy b. -19xy c. 5xy
6. Reduce: 6x² - 4x²
a. 10x² b. 2x² c. -2x²

®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999
Plaza Playa de Aro, 3, 1º DO 44002-TERUEL