FACTORING SPECIAL PRODUCTS - FACTORING EXPRESSIONS USING ALGEBRA FORMULAS

Algebra Factoring before Factoring Special Products,
if you have not already done so.

There, we explained Factors or Divisors,
Factoring Polynomials, Prime Polynomial etc.

That knowledge is a prerequisite here.

There, we have seen some special products as
Algebra Formulas and we have also seen their proofs.

Now we make use of those Formulas
to find the factors, given the product.

We list out the same Formulas
with L.H.S. and R.H.S. reversed.

We have to remember these Formulas from
L.H.S. to R.H.S. and from R.H.S. to L.H.S.
and be able to apply them in both directions.

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Algebra Formulas used for Factoring Special Products

Formula 1 in Algebra Factoring
to be used in Factoring Special Products :

Polynomial expressible as Square of Sum of Two Terms:

a2 + 2ab + b2 = (a + b)2

Formula 2 in Algebra Factoring
to be used in Factoring Special Products :

Polynomial expressible as Square of Difference of Two Terms:

a2 - 2ab + b2 = (a - b)2

Formula 3 in Algebra Factoring
to be used in Factoring Special Products :

Difference of Two Squares as Product of Sum and Difference:

a2 - b2 = (a + b)(a - b)

Formula 4 in Algebra Factoring:

Sum of Two Cubes as Product of Two Factors:

a3 + b3 = (a + b)(a2 - ab + b2)

Formula 5 in Algebra Factoring:

Difference of Two Cubes as Product of Two Factors:

a3 - b3 = (a - b)(a2 + ab + b2)

Formula 6 in Algebra Factoring:

Polynomial expressible as Cube of Sum of Two Terms:

a3 + 3a2b + 3ab2 + b3 = a3 + 3ab(a + b) + b3 = (a + b)3

Formula 7 in Algebra Factoring:

Polynomial expressible as Cube of Difference of Two Terms:

a3 - 3a2b + 3ab2 - b3 = a3 - 3ab(a - b) - b3 = (a - b)3

Formula 8 in Algebra Factoring:

Polynomial expressible as Square of Sum of Three Terms:

a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2

Formula 9 in Algebra Factoring:

Sum of Cubes of Three Terms Minus three times the product of the three terms as Product of Two Factors:

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

Formula 10 in Algebra Factoring:

Simple Quadratic Polynomial as Product of Two Factors:

x2 + x(a + b) + ab = (x + a)(x + b)

Formula 11 in Algebra Factoring:

General Quadratic Polynomial as Product of Two Factors:

acx2 + x(ad + bc) + bd = (ax + b)(cx + d)

Formula 12 in Algebra Factoring:

Simple Cubic Polynomial as Product of Three Factors:

x3 + x2(a + b + c) + x(ab + bc + ca) + abc = (x + a)(x + b)(x + c)

Here a, b, c, d, x are all real numbers.

Each of the letters in fact represent a TERM.

e.g. The above Formula 1 can be stated as

(First term)2 + 2(First term)(Second term) + (Second term)2
= (First term + Second term)2

Similarly in other Formulae also, we can
replace each of the letters by a TERM.

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Solved Examples in Factoring Special Products :

The following Links take you to the Solved
Examples as well as Exercise problems
on Factoring Special Products.

Set 1 of Solved Examples and Exercise problems

Set 2 of Solved Examples and Exercise problems

Set 3 of Solved Examples and Exercise problems

Progressive Learning of Math : Factoring Special Products

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