Timmy2Turnt
contestada

Factor this expression completely, and, then, place the factors in the proper location on the grid. Place the binomial factor first. x 3 + y 3

Respuesta :

kerriamolden
  (x-y)(x^2+xy+y^2) 
_______________ 

the first parentheses contain the cubed root of both the terms so x and y respectively. second parentheses follows the formula (a^2 + ab + b^2) 
x corresponds to a and y corresponds to b. The signs are what change depending on what the original equation is. Since the original is a subtraction then the signs are -/+/+. you can remember it using the acronym SOAP. (S = same, O = opposite, AP = always positive) So the first sign is x - y (same as subtraction from original), the second and third are x^2 + xy + y^2 (opposite is a plus, and the last sign is always a positive)

Answer:

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

Step-by-step explanation:

The given expression is

[tex]x^{3}+y^{3}[/tex]

This expression represents the sum of two perfect cubes, which is factorize as this product

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

We can demonstrate this factorization by multiplying the product

[tex](a+b)(a^{2}-ab+b^{2})=a^{3}-a^{2}b+ab^{2}+a^{2}b-ab^{2}+b^{3}=a^{3}+b^{3}[/tex]

Therefore, the answer is

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

Otras preguntas