The factors of $x^2+4 y^2+4 y-4 x y-2 x-

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Target Exam

CUET

Subject

General Aptitude Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

The factors of $x^2+4 y^2+4 y-4 x y-2 x-8$ are:

Options:

$(x-2 y-4)(x-2 y+2)$

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

$(x+2 y-4)(x+2 y+2)$

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

Correct Answer:

$(x-2 y-4)(x-2 y+2)$

Explanation:

= x²+ 4y²− 4xy + 4y − 2x − 8
= (x−2y)² + 2(2y−x) − 8
= (x−2y)² −2(x−2y) − 8
Let A = x−2y

Thus A² − 2A − 8
= (A−4)(A+2)

Re-substitute the value of A
Thus x² + 4y² + 4y − 4xy − 2x − 8= (x−2y−4)(x−2y+2)