Rules for Signs of Products
Algebra Help: Section 2.13
Learn about the rules which govern the signs of products, in algebra.
The following four examples demonstrate the law which governs the sign of a product.
1. Multiply a by b.
OPERATION:
+a +b ___ +ab
ANALYSIS -
The plus sign of the multiplier,
indicates that the multiplicand, +a
should be added to zero b times.
Therefore the result is positive or +ab.
2. Multiply -a
by -b.
OPERATION:
Multiplicand -a
Multiplier -b
___
+ab
ANALYSIS -
The minus sign of the multiplier, -b, indicates that the multiplicand,
-a should be subtracted from zero,
b times.
Subtraction of a negative results in a positive value, +ab.
3. Multiply a by -b.
OPERATION:
+a -b ___ -ab
ANALYSIS -
The minus sign of the multiplier, b
indicates that the multiplicand a should be
subtracted from zero b times.
The result -a-a-a...
changes the product's sign.
For example substitute a with 3 and b with 2.
The product; 3 * (-2) = -6.
4. Multiply -a by b.
OPERATION:
Multiplicand -a
Multiplier +b
___
-ab
ANALYSIS -
The plus sign of the multiplier, b
indicates that the multiplicand, -a,
should be added to zero b times.
Adding a negative value to zero, results in a negative.
Comparison
Comparing the four examples, observe that multiplying two like signs results in positive products. Multiplying two unlike signs results in negative products.
RULE -
- Multiply the coefficients of two terms together for the coefficient of the product.
- Write all literals. Give each literal the sum of its exponents.
- If the signs of two terms are alike, then the product's positive.
- If the signs of two terms are different, then the product's negative.
NOTE - The value of the product will be the same in whatever order the factors are written. Most algebraists prefer to arrange letters in alphabetical order.
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Help with Algebra Homework
Free tutorials provide math help for math problems. Tutorials start with algebra 1. Algebra tutorials include word problems related to algebra topics, as they're introduced. See the menu, above for algebra math equations, and explanation, by section.
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Windows games, in progress, work with this set of free tutorials, modified
from the public domain text book titled,
New Elementary Algebra
containing the rudiments of the science for schools and academies.
By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
