Question

5. Factorise :
(i) 49(x - y)2 -25(x +
y)2​

Answer 1

Answer:

24 (x - y)^2

Step-by-step explanation:

49(x - y)^2 - 25(x + y)^2

7^2 (x - y)^2 - 5^2 (x + y)^2 (writing 49 as 7 square and 25 as 5 square)

{7^2 (x - y)^2} - {5^2 (x + y)^2}

{7(x-y)}^2 - {5(x+y)}^2 (removing the square common outside both the terms and making the expression equivalent to the formula of x square - y square)

{7(x-y) + 5(x-y)} {7(x-y) - 5(x-y)}

(applying the formula x^2 - y^2 = (x+y) (x-y))

{7x -7y + 5x - 5y} {7x -7y - 5x + 5y} (simplifying by opening bracket - remember the second part 5 opens with a negative sign and changes all the sign in the bracket)

{7x + 5x - 7y - 5y} {7x - 5x - 7y + 5y} (rearranging to like terms)

{12x - 12y} {2x - 2y} (simplifying)

{12 (x -y)} x {2 (x - y)}

12 x 2 x (x - y)^2

24 (x - y)^2

I hope it helps