Special products is a Mathematical term in which factors are combined to form products. It is called "special" because they do not need long solutions.
Square of a Binomial
- this special product results into Perfect Square Trinomial (PST)
(a+b)^2= a^2 + 2ab + b^2
(a-b)^2= a^2- 2ab + b^2
Product of a Binomial and Trinomial:
Another type of polynomial multiplication problem is the product of a binomial and trinomial. Using the distributive property, each term in the binomial must be multiplied by each of the terms in the trinomial.
Sum and Difference of two Binomial:
The product of the binomial sum and difference is equal to the square of the first term minus the square of the second term. In binomial products of the form (x + y)(x − y), one binomial is the sum of two terms and the other is the difference of the same two terms. Consider (x + 2)(x − 2). Thus, the product of x + y and x − y is the difference of two squares.
Cube of a Binomial:
For cubing a binomial we need to know the formulas for the sum of cubes and the difference of cubes.
Sum of cubes:
The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= a3 + 3ab (a + b) + b3
Difference of cubes:
The difference of a cubed of two binomial is equal to the cube of the first term, minus three times the square of the first term by the second term, plus three times the first term by the square of the second term, minus the cube of the second term.
Answers & Comments
Answer:
DESCRIPTION OF SPECIAL PRODUCTS:
Special products is a Mathematical term in which factors are combined to form products. It is called "special" because they do not need long solutions.
Square of a Binomial
- this special product results into Perfect Square Trinomial (PST)
(a+b)^2= a^2 + 2ab + b^2
(a-b)^2= a^2- 2ab + b^2
Product of a Binomial and Trinomial:
Another type of polynomial multiplication problem is the product of a binomial and trinomial. Using the distributive property, each term in the binomial must be multiplied by each of the terms in the trinomial.
Sum and Difference of two Binomial:
The product of the binomial sum and difference is equal to the square of the first term minus the square of the second term. In binomial products of the form (x + y)(x − y), one binomial is the sum of two terms and the other is the difference of the same two terms. Consider (x + 2)(x − 2). Thus, the product of x + y and x − y is the difference of two squares.
Cube of a Binomial:
For cubing a binomial we need to know the formulas for the sum of cubes and the difference of cubes.
Sum of cubes:
The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= a3 + 3ab (a + b) + b3
Difference of cubes:
The difference of a cubed of two binomial is equal to the cube of the first term, minus three times the square of the first term by the second term, plus three times the first term by the square of the second term, minus the cube of the second term.