3. Similar terms

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. Are the terms  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

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