Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De determinant $\begin{vmatrix}(x+y)^2 &(x-y)^2 \\x+y & x-y \\\end{vmatrix}$ is gelijk aan	A. 0
	B. 2y(x + y)( x − y )
	C. y( x − y ) (x + y)
	D. −(x + y)²( x − y ) ²
	E. (x²− y²)(x + y)

[ 5-6896 - op net sinds 20.6.12-(E)-30.10.2023 ]

Translation in E N G L I S H

The determinant $\begin{vmatrix}(x+y)^2 &(x-y)^2 \\x+y & x-y \\\end{vmatrix}$ is equal to	A. 0
	B. 2y(x + y)( x − y )
	C. y( x − y ) (x + y)
	D. −(x + y)²( x − y ) ²
	E. (x²− y²)(x + y)

Oplossing - Solution

$\begin{vmatrix}(x+y)^2 &(x-y)^2 \\x+y & x-y \\\end{vmatrix}=(x+y)(x-y)\cdot \begin{vmatrix}x+y & x-y \\1 & 1\\\end{vmatrix} \\=(x^2-y^2)(x+y-x+y)=(x-y)(x+y).2y$