= {2(x+y)}^2 - 2*(7y)(x+y) + (7y)^2The above equation is of form a^2 - 2ab + b^2 which is equal to (a-b)^2where a = 2(x+y) and b = 7yHence, {2(x+y)}^2 - 2*(7y)(x+y) + (7y)^2 = {2(x+y) - 7y}^2 a^2 - 2ab + b^2 = (a - b)^2

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Factorising 4(x y)^2 - 28y(x y) + 49y^2

To factorise the given expression, we need to look for common factors and use algebraic techniques to simplify it. Let's break it down step by step:

Step 1: Identify common factors
In the given expression, we can see that both terms have a common factor of (x y). Therefore, we can factor out (x y) from both terms as follows:

4(x y)^2 - 28y(x y) + 49y^2 = (x y)(4(x y) - 28y + 49y^2)

Step 2: Simplify the remaining expression
Now, let's simplify the remaining expression within the brackets:

4(x y) - 28y + 49y^2

Step 3: Rearrange the terms
To make it easier to factorise, let's rearrange the terms in descending order of powers:

49y^2 - 28y + 4(x y)

Step 4: Determine factors of the quadratic expression
Next, we need to determine the factors of the quadratic expression 49y^2 - 28y + 4(x y). We can do this by using the quadratic formula or by factoring.

The quadratic expression can be factored as follows:

49y^2 - 28y + 4(x y) = (7y - 2(x y))(7y - 2(x y))

Step 5: Combine the factors
Finally, we can combine the factors from step 1 and step 4 to obtain the final factorised form of the given expression:

4(x y)^2 - 28y(x y) + 49y^2 = (x y)(7y - 2(x y))^2

So, the factorised form of the given expression is (x y)(7y - 2(x y))^2.