Question

factorise (2x + y)² - (2x - y)²​

Answer 1

Answer:

8xy

$(2x + y) {}^{2} = 4x {}^{2} + 4xy + y {}^{2} \\ (2x - y) {}^{2} = 4x {}^{2} - 4xy + y {}^{2} \\ (2x + y) {}^{2} - (2x - y) {}^{2} = 8xy$

Answer 2

Step-by-step explanation:

It is given that,

${(2x + y)}^{2} - {(2x - y)}^{2}$

Now Using Identities,

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

And

$({x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

Put,

$4 {x}^{2} + {y}^{2} + 4xy - (4 {x}^{2} + {y}^{2} - 4xy)$

Open the Brackets,

$4 {x}^{2} + {y}^{2} + 4xy - 4 {x}^{2} - {y}^{2} + 4xy$

Cutting Common things,

We get

$4xy + 4xy$

$8xy$

Hence Solved ,

Hope it Helpsss!!!