Factorise : ab(x^2 + y^2) - xy(a^2 + b^2)

ab(x 2 \+ y 2 ) \- xy(a 2 \+ b 2 ) = abx 2 \+ aby 2 \- xya 2 \- xyb 2 = (abx 2 \- xya 2 ) \+ (aby 2 \- xyb 2 ) = (abx 2 \- a 2 xy) \+ (aby 2 \- b 2 xy) = ax(bx \- ay) \+ by(ay \- bx) = ax(bx \- ay) \- by(bx \- ay) = (bx \- ay)(ax \- by) Hence,ab(x 2 \+ y 2 ) \- xy(a 2 \+ b 2 ) = (bx \- ay)(ax \- by)

Mathematics

Factorise :
ab(x² + y²) - xy(a² + b²)

Factorisation

8 Likes

Answer

ab(x² + y²) - xy(a² + b²)

= abx² + aby² - xya² - xyb²

= (abx² - xya²) + (aby² - xyb²)

= (abx² - a²xy) + (aby² - b²xy)

= ax(bx - ay) + by(ay - bx)

= ax(bx - ay) - by(bx - ay)

= (bx - ay)(ax - by)

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

Answered By

5 Likes

Mathematics

Factorise :
ab(x² + y²) - xy(a² + b²)

Factorisation

Answer

Related Questions

Factorise :
xy² + (x - 1)y - 1

Factorise :
(ax + by)² + (bx - ay)²

Factorise :
m - 1 - (m - 1)² + am - a

Factorise :
25(2x - y)² - 16(x - 2y)²

Mathematics

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

Factorisation

Answer

Related Questions

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

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

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

Factorise :25(2x - y)2 - 16(x - 2y)2

Factorise :
ab(x² + y²) - xy(a² + b²)

Factorise :
xy² + (x - 1)y - 1

Factorise :
(ax + by)² + (bx - ay)²

Factorise :
m - 1 - (m - 1)² + am - a

Factorise :
25(2x - y)² - 16(x - 2y)²