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MATH NOTES
Multiplying Algebraic Expressions with Tiles - 3.2.2
The area of a rectangle can be written
width and length or as a
different ways. It can be written as a
of its
of its parts. For example, the area of the shaded rectangle at right
can be written two ways:
=
area as a product =
x2+6x+8
area as a sum
HODS AND MEANINGS
MATH NOTES
Vocabulary for Expressions- 3.2.3
A mathematical
is a combination of numbers, variables, and operation
symbols. Addition and subtraction separate expressions into parts called
. For
example, 4x2 - 3x+ 6 is an expression. It has three tenns: 4x2, 3x, and 6. The
are 4 and
3. 6 is called a
A one-variable
is an expression which only has terms of the form:
(any real number) X(whOle number)
For example, 4x2 3X1 + 6X° is a polynomials, so the simplified form, 4x2 -- 3x + 6 is a polynomial.
±
The functionf(x) = 7xs + 2.5x3 2 x + 7 is a polynomial function.
The following are not polynomials: 2x 3, ':z-2 and ÿ€ÿ
A
is a polynomial with only two terms, for example, x3 - 0.5x and 2x + 5.
AND MEANINGS
MATH NOTES
Properties of Real Numbers - 3.2.4
The legal tiles moves have formal mathematical names, called the
The Commutative Property states that when
numbers or terms, order is not important. That is:
or
two or more
a+b-b+a For example, 2+7=7+2
a'b=b.a
For example, 3-5 5-3
However, subtraction and division are
commutative, as shown below.
7-2¢2 7since5¢ 5
50+ 10€ 10+50 since 5 ÿ0.2
The
states that when adding or multiplying three or more
important. That is:
numbers or terms together, grouping is
(a + b) + c = a + (b + c) For example, (5 + 2) + 6 = 5 + (2 + 6)
(a'b)-c =a'(b'c)
For example, (5.2).6=5.(2.6)
However, subtraction and division are not associative, as shown below.
(5 2) 3€5-(2-3) since0¢6
(20 + 4) + 2 € 20 +(4 + 2) since 2.5 € 10
The
states that adding
same expression. That is:
a+0=a
The
number
1.a=a
For example, 1 . 6 = 6
states that for every number
there is a
such that a +(a) -- 0. A common name used for the additive inverse is the
• That is, -a is the opposite of a. For example, 3 + (-3) = 0 and -5 + 5 = 0
The
number
For example, 6 + 0 = 6
states that muitiplying any expression by
gives the same expression. That is:
The
to any expression gives the
states that for every nonzero number a there is a
a-±=l.
such that u
A common name used for the multiplicative inverse is the
±
• That is, a is the reciprocal of a. For example,
6"ÿ=I