Factorise the following: (ax + by) 2 + (bx - ay) 2 .

(ax + by) 2 + (bx - ay) 2 = a 2 x 2 + b 2 y 2 + 2axby + b 2 x 2 + a 2 y 2 - 2axby = a 2 x 2 + b 2 x 2 + b 2 y 2 + a 2 y 2 = x 2 (a 2 + b 2 ) + y 2 (b 2 + a 2 ) = (x 2 + y 2 )(a 2 + b 2 ). Hence, (ax + by) 2 + (bx - ay) 2 = (x 2 + y 2 )(a 2 + b 2 ).

Mathematics

Factorise the following:
(ax + by)² + (bx - ay)².

Factorisation

51 Likes

Answer

(ax + by)² + (bx - ay)²

= a²x² + b²y² + 2axby + b²x² + a²y² - 2axby

= a²x² + b²x² + b²y² + a²y²

= x²(a² + b²) + y²(b² + a²)

= (x² + y²)(a² + b²).

Hence, (ax + by)² + (bx - ay)² = (x² + y²)(a² + b²).

Answered By

23 Likes

Mathematics

Factorise the following:
(ax + by)² + (bx - ay)².

Factorisation

Answer

Related Questions

Factorise the following:
x² - x(a + 2b) + 2ab

Factorise the following:
ab(x² + y²) - xy(a² + b²)

Factorise the following:
a³ + ab(1 - 2a) - 2b².

Factorise the following:
3x²y - 3xy + 12x - 12.

Mathematics

Factorise the following:(ax + by)2 + (bx - ay)2.

Factorisation

Answer

Related Questions

Factorise the following:x2 - x(a + 2b) + 2ab

Factorise the following:ab(x2 + y2) - xy(a2 + b2)

Factorise the following:a3 + ab(1 - 2a) - 2b2.

Factorise the following:3x2y - 3xy + 12x - 12.

Factorise the following:
(ax + by)² + (bx - ay)².

Factorise the following:
x² - x(a + 2b) + 2ab

Factorise the following:
ab(x² + y²) - xy(a² + b²)

Factorise the following:
a³ + ab(1 - 2a) - 2b².

Factorise the following:
3x²y - 3xy + 12x - 12.