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 Depdendent Variable

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 Dependent Variable

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# Special Factoring

Objectives: To factor the difference
of two squares, to factor Perfect
Square Trinomials, and to factor the
sum or difference of two cubes.

Review of 7.1 & 7.2

ο Define factoring.
ο How do we check our answer after
ο factoring?
ο Factor:
ο A) k2 – 11kh + 28h2
ο B) 4x2 + 2x - 6

Review

ο Multiply using FOIL:
(x – 3) (x + 3).
x2 + 3x – 3x - 9

Remember: the outside/inside terms cancel b/c they
are opposite terms.

ο Multiply: (y + 2)(y – 2)

ο This answer is a special case called the

DIFFERENCE OF TWO SQUARES
(a.k.a. DOTS).

Factoring the Difference of
Two Squares (DOTS)

ο Clue 1: usually only 2 terms
ο Clue 2: _________ sign
ο Clue 3: _______ terms are perfect squares

ο General Form: x2 – y2 = (x + y)(x - y)

ο MEMORIZE THESE PERFECT SQUARES:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,
169, 196, 225, 256,…,
400,…,625,…900,…,10000

Examples – Factor.

ο a) x2 – 25
ο b) 3a2 – 48
ο c) 169x2 – y2
ο d) 81a2 – 121b2

Think, pair, share…

ο e) 9x2 – z4
ο f) 4a4 – 49b8
ο g) 5y3 – 320y
ο h) (m - 2)2 – 100

REVIEW
The Square of a Binomial

ο Multiply (m – 4)2.

ο Multiply (5n + 3)2.

What to look for…
Ax2 + Bx + C

ο Clue 1: A & C are _________, perfect
squares.

ο Clue 2: B is the square root of A times
the square root of C, doubled.

If these two things are true, the trinomial is
a Perfect Square Trinomial (PST) and can
be factored as (x + y)2 or (x – y)2.

General Form of Perfect
Square Trinomials

ο x2 + 2xy + y2 = (x + y)2
or
ο x2 – 2xy + y2 = (x - y)2

ο Note: When factoring, the sign
in the binomial is the _______
as the sign of B in the trinomial.

Just watch and think.

ο Ex) x2 + 12x + 36
ο What’s the square root
of A? of C?
ο Multiply these and
double. Does it = B?
ο Then it’s a Perfect
Square Trinomial!

ο Solution: (x + 6)2

ο Ex) 16a2 – 56a + 49
ο Square root of A?
of C?
ο Multiply and
double…
ο = B?

ο Solution: (4a – 7) 2

Examples

ο A) x2 + 8x + 16
ο B) 9n2 + 48n + 64
ο C) 4z2 – 36z + 81

Think, pair, share…

ο D) 25c2 – 20c + 4 – d2
ο E) 9a2 – 24a + 16 – b2

What if the leading term has
an odd power?

ο The problem could be the sum or
difference of two cubes. (page 389)

Factoring the Difference or
Sum of Two Cubes

ο Clue 1: usually only 2 terms
ο Clue 2: both terms are perfect cubes

MEMORIZE THESE PERFECT CUBES:
1, 8, 27, 64, 125, 216,…1000

General Form of Factoring
Cubes

x3 – y3 = (x - y)(x2 + xy + y2)
or
x3 + y3 = (x + y)(x2 - xy + y2)

Examples

ο A) x3 + 64
ο B) 8n3 – 27
ο C) 125a3 + b3

Think, pair, share…

ο D) 216c3d3 + 1
ο E) 4y3 – 500z3