Question

Factorize

9z²-x²+4xy-4y²

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Answer 1

9z²-(x²-4xy+4y²)

= 9z²-{(x)²-2.x.2y+(2y)²}

= 9z²-(x-y)²(3z)²-(x-y)²

= (3z+x-y)(3z-x+y)

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Answer 2

Step-by-step explanation:

Correct option is

B

[(x−2y−3z)(x−2y+3z)]

The given expression x

2

+4y

2

−9z

2

−4xy can be factorized as shown below:

x

2

+4y

2

−9z

2

−4xy

=(x

2

+4y

2

−4xy)−9z

2

=[x

2

+(2y)

2

−(2×x×2y)]−9z

2

=(x−2y)

2

−9z

2

(∵(a−b)

2

=a

2

+b

2

−2ab)

=(x−2y)

2

−(3z)

2

=(x−2y−3z)(x−2y+3z)(∵a

2

−b

2

=(a−b)(a+b))

Hence, x

2

+4y

2

−9z

2

−4xy=(x−2y−3z)(x−2y+3z).