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The factored form of $9 z 2 − x 2 − 4 y 2 + 4 x y$ is [[1]].

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answer is ( 3 Z + X − 2 Y ) ( 3 Z − X + 2 Y ).

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Detailed Solution

The factored form of

9 z 2 − x 2 − 4 y 2 + 4 x y

(3 z + x − 2 y) (3 z − x + 2 y)

.
Here, an algebraic expression is given as

9 z 2 − x 2 − 4 y 2 + 4 x y

.
The algebraic expression can be regrouped as follows,

9 z 2 − x 2 − 4 y 2 + 4 x y ⇒ 3 z 2 − x 2 + 4 y 2 − 4 x y

Now, we use the following identity

a 2 + b 2 − 2 a b = a − b 2

3 z 2 − x 2 + (2 y) 2 − 2 (x) (2 y) ⇔ 3 z 2 − x − 2 y 2

To factorize this expression, we can use the identity

a 2 − b 2 = a + b a − b

.
So, using the identity, the expression

3 z 2 − x − 2 y 2

, can be written as follows,

3 z 2 − x − 2 y 2 = 3 z + x − 2 y 3 z − x − 2 y = 3 z + x − 2 y 3 z − x + 2 y

So, the factored form of

9 z 2 − x 2 − 4 y 2 + 4 x y

(3 z + x − 2 y) (3 z − x + 2 y)

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