ALGEBRA FORMULAS - SPECIAL PRODUCTS, EXAMPLES, EXERCISE, LINKS TO OTHER FORMULAS
Polynomials before Algebra Formulas,
if you have not already done so.
There, we discussed definition, simplified form, addition,
subtraction, multiplication etc. of Polynomials.
That knowledge is a prerequisite here.
Here, We deal with Some Special Products in Polynomials.
Certain products of Polynomials occur more often
in Algebra. They are to be considered specially.
These are to be remembered as Formulas in Algebra.
Remembering these formulas in Algebra is as important
as remembering multiplication tables in Arithmetic.
We give a list of these Formulas and Apply
them to solve a Number of problems.
We give Links to other Formulas in Algebra.
Here is the list of Formulas in
Polynomials which are very useful in Algebra.
Formulas in Polynomials :
Algebra Formula 1 in Polynomials: Square of Sum of Two Terms:
( + a ) b 2 = a 2 + 2 a + b b 2 Algebra Formula 2 in Polynomials: Square of Difference of Two Terms:
( - a ) b 2 = a 2 - 2 a + b b 2 Algebra Formula 3 in Polynomials: Product of Sum and Difference of Two Terms:
( + a )( b - a ) = b a 2 - b 2 Algebra Formula 4 in Polynomials: Product giving Sum of Two Cubes:
( + a )( b a 2 - a + b b 2) = a 3 + b 3 Algebra Formula 5 in Polynomials: Product giving Difference of Two Cubes:
( - a )( b a 2 + a + b b 2) = a 3 - b 3 Algebra Formula 6 in Polynomials: Cube of Sum of Two Terms:
( + a ) b 3 = a 3 + 3 a 2 + 3 b a b 2 + b 3 = a 3 + 3 a ( b + a ) + b b 3 Algebra Formula 7 in Polynomials: Cube of Difference of Two Terms:
( - a ) b 3 = a 3 - 3 a 2 + 3 b a b 2 - b 3 = a 3 - 3 a ( b - a ) - b b 3 Algebra Formula 8 in Polynomials: Square of Sum of Three Terms:
( + a + b ) c 2 = a 2 + b 2 + c 2 + 2 a + 2 b b + 2 c c a Formula 9 in Polynomials: Product giving Sum of Cubes of Three Terms minus Three times the Product of the Three Terms:
( + a + b )( c a 2 + b 2 + c 2 - a - b b - c c ) = a a 3 + b 3 + c 3 - 3 a b c Formula 10 in Polynomials: Product of Two Simple Linear Polynomials:
( + x )( a + x ) = b x 2 + ( x + a ) + b a b Formula 11 in Polynomials: Product of Two General Linear Polynomials:
(a + x )(c b + x ) = d a c x 2 + ( x a + d b ) + c b d Formula 12 in Polynomials: Product of Three Simple Linear Polynomials:
( + x )( a + x )( b + x ) = c x 3 + x 2( + a + b ) + c ( x a + b b + c c ) + a a b c
, a , b , c , d are all real numbers. x Each of the letters in fact represent a TERM. e.g. The above Formula 1 can be stated as (First term + Second term) 2 = (First term) 2 + 2(First term)(Second term) + (Second term) 2 Similarly in other Formulas also, we can replace each of the letters by a TERM.
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Proofs of Formulas in Polynomials :
Proofs of the above listed Formulas
are given at the following Links.
Proofs of First Six Formulas
Proofs of Last Six Formulas
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Solved Examples on Formulas
The following Links take you to the
Solved Examples and Exercise problems on application of the Formulas.
Set 1 of Solved Examples and Exercise problems
Set 2 of Solved Examples and Exercise problems
Set 3 of Solved Examples and Exercise problems
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Other Math Formulas
The Following Links take you to other Math Formulas.
Formulas in Exponents
Formulas in Logarithms