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Botes on Bloebra.
Algebra is that branch of mathematics in which the quan-
tities are denoted by letters and the operations to be performed
upon them are indicated by signs. The same signs are used to
indicate the same operations as in arithmetic.
Signs of Quantity and Signs of Operation.
If a quantity is written a 4 (
—
b), the sign that precedes the
parenthesis is called the sign of operation, and the sign within
the parenthesis is called the sign of quantity with respect to by
but expressions of this kind can be reduced to have only one
sign. Thus, a 4 (— b) = a — b and this final sign is called the
essential sign.
a + (+ b) = a 4 b.
a -\- ( — b) = a — b.
a — (4 b) = a — b.
a — (—b) = a -h b.
Thus, when the sign of operation and the sign of quantity
are alike the essential sign is +, but if they are unlike the es-
sential sign is —
.
In multiplying any two quantities, like signs in the two
factors give -f in the product, but unlike signs in the two factors
give — in the product; thus, (+ a) X (— b) = — ab, and (
—
a)
X (— b) = ab.
In division, like signs in dividend and divisor give + in the
quotient, but unlike signs in dividend and divisor give — in the
quotient; thus:
— a a
— a , a
— b b
Useful Formulas and Rules in Algebra.
The following rules are very useful to remember in solv-
ing practical problems in algebra. Let a and b represent any
two quantities; then a -\- b will represent their sum and a — b
their difference; then (a + b) X (a 4 b) = a’2
4 2 ab 4 b2
.
{a 4 b) X (a 4 b) is also written (a 4 b)
2
.
(63)
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