Question

Multiply..........(x + y)( {x}^{2} - xy + {y}^{2} )​

Answer 1

To multiply the expression (x + y)(x^2 - xy + y^2), we use the distributive property to individually multiply each term in the first expression by each term in the second expression. Then, we combine like terms to simplify the result.

Step-by-step explanation:

To multiply the expression (x + y)(x^2 - xy + y^2), we can use the distributive property. This property states that when we have a sum of terms multiplied by another term, we can multiply each term individually and then add the results.

1. Multiply (x) by each term in the second expression: x * x^2 = x^3, x * (-xy) = -x^2y, and x * y^2 = xy^2.
2. Then, multiply (y) by each term in the second expression: y * x^2 = x^2y, y * (-xy) = -xy^2, and y * y^2 = y^3.
3. Finally, combine like terms: x^3 + (-x^2y) + xy^2 + x^2y + (-xy^2) + y^3 = x^3 + y^3.

Therefore, the resulting expression is x^3 + y^3.