Question

Multiply x^2 +2y and x^3 - 2xy + y^3. Then find the value of the product for x =1 and y = -1. *

Answer 1

Answer:

$= ({x}^{2} + 2y)( {x}^{3} - 2xy + {y}^{3} ) \\ \\ = {x}^{2} ( {x}^{3} - 2xy + {y}^{3} ) + 2y( {x}^{3} - 2xy + {y}^{3} ) \\ \\ = {x}^{5} - 2 {x}^{3} + {x}^{2} {y}^{3} + 2 {x}^{3} y - 4x {y}^{2} + 2 {y}^{4} \\ \\ substituting \: \: the \: \: \: value \: \: \: of \: \: x \: \: \: and \: \: \: y \\ \\ = {1}^{5} - 2 \times {1}^{3} + {1}^{2} \times { - 1}^{3} + 2 \times {1}^{3} \times - 1 - 4 \times 1 \times { - 1}^{2} + 2 \times { - 1}^{4} \\ \\ = 1 - 2 + ( - 1) + ( - 2) - 4 + ( - 2) \\ \\ = 1 - 2 - 1 - 2 - 4 - 2 \\ \\ = - 10$