04 Special Products and Factoring

7/27/2019 04 Special Products and Factoring

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SpecialProducts


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A. Product of the Sum and Difference of Two Terms

22))(( y x y x y x

The product of the sum and difference of twoterms is equal to the square of the first term minusthe square of the second term.


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B. Square of Binomial

222

2)( y xy x y xThe square of a binomial is equal to the

square of the first term plus twice the product of the two terms plus the square of the second term.

222 2)( y xy x y x


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C. Cube of Binomial

The cube of a binomial is equal to the cubeof the first term plus thrice the product of thesecond term and the square of the first term plus

thrice the product of the first term and the squareof the second term plus the cube of the secondterm.

32233

33)( y xy y x x y x

32233 33)( y xy y x x y x


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D. Product of Two Binomials with LikeTerms

22 )())(( bdy xybcad acxdycxbyax

The product of two binomials with like termsis equal to the product of the first terms of thebinomials plus the sum of the products of the twoouter terms and two inner terms plus the productof the last terms of the binomials (FOIL Method).


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The product of a binomial (x + y) and atrinomial (x 2 xy + y 2) is simply equal to the sum of

the cubes of the first term and second term of thebinomial.

3322

))(( y x y xy x y x

3322 ))(( y x y xy x y x

E. Product of Binomial (x y) andTrinomial (x 2 xy + y 2)


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F. Square of Trinomial

yz xz xy z y x z y x 222)( 2222

The square of a trinomial is equal to the sumof the squares of each term in the trinomial plustwice the product of the first and second term plustwice the product of the first and third term plustwice the product of the second and third term.


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G. Square of Polynomial

The square of a polynomial is equal to thesum of the squares of each term in the polynomialplus twice the algebraic sum of the products

obtained by multiplying any two terms of thepolynomial.

nnn

nn

x x x x x x x x x x

x x x x x x x x x x

14232131

2122

322

21

2321

2...222...2

2...)...(


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Factoring- is the process of finding theprime factors of an expression


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Difference of Two Squares

))((22 y x y x y x

1. 25x 4 9y 2

2. 121w 2 100

3. 81z4 64a

4

4. 49x 2 9y 2


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Sum and Difference of

Two Cubes

1. 8m 3n 3 125

2. 27x 3 + 64y 3

3. 125x3 y

3

4. 25m 6 + 200m 3n 3

))(( 2233 y xy x y x y x))(( 2233 y xy x y x y x


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Perfect Square Trinomial

1. 9x 2 + 6xy + y 2

2. 9a 2 42ab + 49b 2

3. 36a4x

2+ 84a

2bxy

3+ 49b

2y

6

4. 144a 5b 3 240a 3b 2 + 100ab

222 )(2 y x y xy x

222 )(2 y x y xy x


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Quadratic Trinomial

1. x 2 7x + 12

2. 2x 2 xy 55y 2

3. 25a2

+ 21a 44. 14p 2q 2 23pqr 66r 2

))(()( 22 dycxbyaxbdy xybcad acx


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Factoring by Grouping

1. 2xy + 6y + x + 3

2. 4a 2 4ab + b 2 + 2a b

3. 6ac 4ad + 15bc 10bd

4. 8p 3 10p 2q 28pr + 35qr

04 Special Products and Factoring

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