Simplify $(x-y+z)^2-(x-y-z)^2$.

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

Simplify $(x-y+z)^2-(x-y-z)^2$.

Options:

$4 x z-4 y z$

$2 x z+2 y z$

$4 y z-4 x z$

$4 x z+4 y z$

Correct Answer:

$4 x z-4 y z$

Explanation:

$(x-y+z)^2-(x-y-z)^2$.

a² - b² = (a + b ) (a - b)

= $(x-y+z)^2-(x-y-z)^2$ = (x - y + z + x - y - z )( x - y + z - x + y + z)

= $(x-y+z)^2-(x-y-z)^2$ = (2x - 2y)(2z)

= $(x-y+z)^2-(x-y-z)^2$ = $4 x z-4 y z$