Factorise ab(x2 + y2) – xy(a2 + b2)

(i) ab(x² + y²) – xy(a² + b²)

(ii) (ax + by)² + (bx – ay)²

Answer :

(i) ab(x² + y²) – xy(a² + b²)

Above question can be written as,

abx² + aby² – xya² – xyb²

Re-arranging the above we get,

abx² – xyb² + aby² – xya²

Take out common in all terms,

bx(ax – by) + ay(by – ax)

bx(ax – by) – ay (ax – by)

(ax – by) (bx – ay)

(ii) (ax + by)² + (bx – ay)²

By expanding the give question, we get,

(ax)² + (by)² + 2axby + (bx)² + (ay)² – 2bxay

a²x² + b²y² + b²x² + a²y²

Re-arranging the above we get,

a²x² + a²y² + b²y² + b²x²

Take out common in all terms,

a² (x² + y²) + b² (x² + y²)

(x² + y²) (a² + b²)

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