Question

*Chose the factors of 4 x² - 36 y² from the given options .* 1️⃣ ( 2x + 6y) (2x -6y ) 2️⃣ 4 (x+y ) (x -y) 3️⃣ 4 (x +3 y) (x - y) 4️⃣ (2x² + 6y² ) (2 x² - 6y²)​

Answer 1

The factors of 4 x² - 36 y² is (1)  ( 2x + 6y ) (2x - 6y )

Given: 4 x² - 36 y²

To Find: The factors of 4 x² - 36 y²

Solution:

The question can be solved by following the formula,

                a² - b² = ( a + b ) × ( a - b )

therefore as the question is 4 x² - 36 y² , we can write it as,

                4 x² - 36 y² = (2x)² - (6y)²

                                    = ( 2x + 6y ) × ( 2x - 6y )

Hence, the factors of 4 x² - 36 y² is (1)  ( 2x + 6y ) (2x - 6y )

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Answer 2

Concept:

A system of equations is a set of numbers and variables with applied mathematical operations.

Given:

4 x² - 36 y²  

Find:

We are asked to find the factors of 4 x² - 36 y².

Solution:

We have,

4 x² - 36 y²  

Now,

We observe that the given equation is following the identity,

i.e.

a² - b² = (a + b) (a - b)

i.e.

4 x² - 36 y²  

Rewrite the above equation,

We get,

4 x² - 36 y²  = (2x)² - (6y)²

Here,

a = 2x and b = 6y

Now,

Using the above-mentioned identity,

(2x)² - (6y)² = (2x + 6y) (2x - 6y)

So,

The factors are (2x + 6y) (2x - 6y).

Hence, the factors of 4 x² - 36 y² are (2x + 6y) (2x - 6y).

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