Like Terms
Like Terms are terms that are
identical in their variable parts, that is, terms that differ in
at most numerical factors.
Examples: 5x² and 3x² , -2xy and 7xy, 7z
and 7z.
Note: 2x² y and 3xy² are unlike terms.
Their variable parts are not identical. The first term involves
the second power of x while the second term involves only the
first power of x or one factor of x. Simialary the first term
involves the first power of y while the second term involves the
second power of y.
Adding and Subtracting Like Terms
The distributive properties ax ± bx = (a
± b)x allow us to add or subtract like terms.
Rule: To add or subtract like terms we add
or subtract their numerical coefficients to obtain the numerical
coefficient of the answer. The variable part of the answer is
identical to the variable part of each of the terms being
combined.
Examples: 5x + 3x = (5 + 3)x = 8x 14ab -
6ab = (14 - 6)ab = 8ab. 5t + t = 5t + 1t = (5 + 1)t = 6t Remember
the understood coefficient of t is one.
Since
(a - b) = 1(a - b) = 1(a) - 1(b)
+(a - b) = +1(a - b) =
+1(a)" - (+1)(b) = a - b and
-(a - b) = -1(a - b) = -1(a) -
(-1)(b) = - a + b
we may state the following rule.
rule:
Rule
If no sign or a plus sign
preceeds a pair of parentheses we may remove the parentheses
without affecting the signs of the terms inside. If a minus sign
preceeds a pair of parentheses we may remove the parentheses
provided we change the sign of every term inside.
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