Factorise : (ax + by)^2 + (bx - ay)^2

(ax \+ by) 2 \+ (bx \- ay) 2 Using the formula [∵ (x \+ y) 2 = x 2 \+ y 2 \+ 2xy] = a 2 x 2 \+ b 2 y 2 \+ 2abxy \+ b 2 x 2 \+ a 2 y 2 \- 2abxy = (a 2 x 2 \+ a 2 y 2 ) \+ (b 2 y 2 \+ b 2 x 2 ) \+ 2abxy\- 2abxy = a 2 (x 2 \+ y 2 ) \+ b 2 (x 2 \+ y 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 :
(ax + by)² + (bx - ay)²

Factorisation

6 Likes

Answer

(ax + by)² + (bx - ay)²

Using the formula

[∵ (x + y)² = x² + y² + 2xy]

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

= (a²x² + a²y²) + (b²y² + b²x²) + 2abxy- 2abxy

= a²(x² + y²) + b²(x² + y²)

= (x² + y²)(a² + b²)

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

Answered By

5 Likes

Mathematics

Factorise :
(ax + by)² + (bx - ay)²

Factorisation

Answer

Related Questions

Factorise :
a² - ab(1 - b) - b³

Factorise :
xy² + (x - 1)y - 1

Factorise :
ab(x² + y²) - xy(a² + b²)

Factorise :
m - 1 - (m - 1)² + am - a

Mathematics

Factorise :(ax + by)2 + (bx - ay)2

Factorisation

Answer

Related Questions

Factorise :a2 - ab(1 - b) - b3

Factorise :xy2 + (x - 1)y - 1

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

Factorise :m - 1 - (m - 1)2 + am - a

Factorise :
(ax + by)² + (bx - ay)²

Factorise :
a² - ab(1 - b) - b³

Factorise :
xy² + (x - 1)y - 1

Factorise :
ab(x² + y²) - xy(a² + b²)

Factorise :
m - 1 - (m - 1)² + am - a