What are the different types of special product?

Answers

These are the difderent types: Square of a binomial, Square of a Trinomial, Cube of a Binomial, Product of sum and difference and Product of a binomial and a special multinomial.

Special products

Square of a Binomial. - this special product results into Perfect Square Trinomial (PST) (a+b)^2= a^2 + 2ab + b^2. ...

Product of sum & difference of two Binomials. -this results to Difference of two squares. (a+b)(a-b) = a^2 - b^2.

Square of Trinomial. - this results to six terms. ...

Product of Binomials.

4{x}^{2}  + 2032 {s}^{2}  - 32{w}^{2}  + 10w + 24{c}^{2}  + 5c - 142 {x}^{2}  + 5x - 12{a}^{2}  - 44 {y}^{2}  - 12y + 96 - 4m \: or \: 4m - 63754 {b}^{2}  - 2510 {x}^{2}  - 302 {y}^{2}  + 8ymultiplied by???{b}^{2}  - 164 {d}^{2}  - 49

Step-by-step explanation:

is it still necessary to put the solution/explanation??

There are special forms of algebraic expressions whose certain conditions which make a polynomial special

Different types of special product

1.Square of Binomial

The square of a binomial consists of;  

a.The square of the first term

b.Twice the product of the first and last terms

c.The square of the last term

Example: ( s + 4) ²

2.Difference of the answer

It is the product of the sum and difference of two terms, in this symbols ( x+y) (x-y) = x² –y².  

3.Cube of Binomial

•To find the cube of a binomial of the form (x+y)3.

a.Find the cube of each term to get the first and the last terms. (x)3, (y)3

b.The second term is three times the product of the square of the first term and the second term. 3(x)2(y)

c.The third term is three times the product of the first term and the square of the second term.  

3(x)(y)²

Hence, (x+y)³ = x³ + 3x²y + 3xy² + y³

•To find the cube of a binomial of the form (x-y)³

a.Find the cube of each term to get the fist and the last terms.  

(x)³, (-y)³

b. the second term is three times the product of the square of the first term and the second term 3(x)²(-y).  

c. the third term is three times the product of the first term and the square of the second term.  

3(x)(-y)²

Hence, (x-y)3  = x³-3x²y + 3xy²–y³

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