I learned in our College Algebra that certain types of products of polynomials are called special products simply because of their
frequent occurrence and use not only in the study of Algebra but also in many
fields study where algebraic processes are applied. Every operations of solving
the following expressions have a certain procedures or rules to be followed.
I discover that you know the rules you can solved any
forms of expressions in Algebra. It is very easy for you to solve it. Same also
in the field of computer programming course. You must follow carefully the
guidelines on how to create a usable and great computer programs. If you know
how to read the source code or the programming language it is very easy for you
to debug the certain program. Always remember one mistake is equal to zero.
But by the way, back to our Algebra. Special products are
as follows:
I. Product of sum and difference of two similar
binomials.
Procedure: Is equal to the square of the first term minus
the square of the second terms.
(a + b) (a - b) = a2 – b2
Example to this:
(2x2p + 3y) (2x2p + 3y) = (2x2p)2
– (3y)2
ANS: = 4x4p2 – 9y2
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II. Square of a binomials.
Procedure: Is equal to the square of the first term plus
twice the product between the first and second term plus the square of the
second term.
(a - b) = (a)2 + 2(a) + (-b) + (-b)2
= 2ab + b2
Example to this:
(2x + 3)2 = (2x2)2 +
2(2x) (3) + (3)2
ANS: = 4x2 + 12x + 9
(5x2p3 – 5y)2 = (5x2p3)2
+ 2(5x2p3) (-5y) + (-5y)2
ANS: = 25x4p6 – 50x2p6y
– 25y2
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III. Cube of a binomials.
Procedure: Is equal to the cube of the first term plus
trice the product of the square of the first term plus and trice the product
between the first term and the square of the 2nd term plus the cube
of the second term.
(a - b)3
= (a)3 + 3(a)2 (-b) + (-b) + 3(a) (-b)2 + b3
= a3 – 3a2b + 3ab2 – b3
(a + b)3 = a3 + 3a2b +
3ab2 + b3
Example to this:
(2x2 – 3)3 = (2x2)3
+ 3(2x2)2 (-3) + 3(2x2) (-3) + (3)3
ANS: = 8x6 – 36x4 + 54x2
– 27
(4p + 5v2)3
= (4p)3 + 3(4p)2 (5v2) +
3(4p) (5v2)2 + (5v2)3
= 64p3 + 3(16p2) (5v2) +
3(4p) (25v4) + 125v6
ANS: = 64p3 + 240p2v2 +
300pv4 + 27v6
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IV. Product of Two Binomials.
The formula looks like this!
a. (x + b) (x + d) = x2 + (b + d)x + b(d)
b. (ax + b) (cx + d) = acx2 + (ad + bc)x +
b(d)
Example to this:
(x - f) (x + 5) = x2 + (-7 + 5)x + (-7)(5)
ANS: = x2 - 2x - 35
(2x + 5) (4x - 3) = (2)(4)x2 + (2)(-3) +
(5)(4)x + (5)(-3)
= 8x2 + (-6 + 20)x + (-15)
ANS: = 8x2 + 14x -15
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V. Square of a Trinomials.
The formula looks like this!
(a + b + c)2 = a2 + b2 +
c2 + 2ab + ac +2bc
Example to this:
(2x2 – 3y3 + 5m)2
= (2x2)2 – (-3y3)2
+ (5m)2 + 2(2x2) + (-3y3) + 2(2x2) + (5m) +
2(-3y3)(5m)
ANS: = 4x4 + 9y6 + 25m2
– 12x2y3 + 20x2m – 30y3m
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I know it will be a big help for those college students that have a College Algebra subject. Here you can learn a lot in terms of algebra. Don’t hesitate to ask questions. Just use our comment box system below.
