Question

(k) 25(x+2y)^2 - 49(x - 2y)^2​

Answer 1

Answer:

8 (12y - x)(3x - y)

Step-by-step explanation:

I'm going to assume that you have to factor this.

Now, it is given :

25(x+2y)^2 - 49(x - 2y)^2​

This can be written as :

5^2 * (x+2y)^2 - 7^2 * (x - 2y)^2​

Using the algebraic identity (a+b) (a-b) we know that this will expand to (a^2 - b^2)

Now, this is already in the form of the latter.

So, the factorized form will be :

[5(x+2y) - 7(x-2y)]^2 * [5(x+2y) + 7(x-2y)]^2

Or,

[5x+10y-7x+14y]^2  * [5x+10y+7x-14y]^2

Or,

[24y - 2x] * [-4y + 12x]

=  (-2x + 24y) (12x - 4y)

Thus, Ans : 8 (12y - x) (3x - y)  {Removing factors such as 4 from (12x-4y) and 2 from (-2x + 24y)