(x%2By)(x%2By)-answer.jpeg "(x+y)(x+y)(x+y) Answer")
The Expansion of (x+y)(x+y)(x+y)
When we multiply three identical binomials, (x+y), we can use the distributive property of multiplication over addition to expand the expression. In this article, we will explore the expansion of (x+y)(x+y)(x+y) and find the resulting polynomial.
Step 1: Multiply the First Two Binomials
First, let's multiply the first two binomials:
(x+y)(x+y) = x(x+y) + y(x+y)
= x^2 + xy + xy + y^2
= x^2 + 2xy + y^2
Step 2: Multiply the Result with the Third Binomial
Now, let's multiply the result with the third binomial:
(x^2 + 2xy + y^2)(x+y) = x^2(x+y) + 2xy(x+y) + y^2(x+y)
= x^3 + x^2y + 2x^2y + 2xy^2 + xy^2 + y^3
= x^3 + 3x^2y + 3xy^2 + y^3
The Final Result
After expanding the expression, we get:
(x+y)(x+y)(x+y) = x^3 + 3x^2y + 3xy^2 + y^3
This is the resulting polynomial after expanding the expression (x+y)(x+y)(x+y).
Conclusion
In this article, we have successfully expanded the expression (x+y)(x+y)(x+y) using the distributive property of multiplication over addition. The final result is a polynomial of degree 3, with terms involving x and y raised to powers of 0, 1, 2, and 3.
