Question

factorise (ax+by)^2+(ax-by)^2 ​

Answer 1

Answer:

(a-b)2 + (a+b)2 = 2(a2+ b2)

= 2(ax^2 + by^2)

Answer 2

Step-by-step explanation:

(ax+by)²+(ax-by)²

= a²x²+b²y²+2axby+a²x²+b²y²-2axby

= 2a²x²+2b²y²

= 2(a²x²+b²y²)

using formula (x+y)² = x²+y²+2xy

(x-y)² = x²+y²-2xy

(ax+by)²+(ay-bx)²

= a²x²+b²y²+2axby+a²y²+b²x²-2aybx

= a²x²+b²y²+a²y²+b²x²

= a²x²+b²x²+b²y²+a²y²

= x²(a²+b²)+y²(a²+b²)

= (a²+b²)(x²+y²)

using formula (x+y)² = x²+y²+2xy

(x-y)² = x²+y²-2xy