$(a x + b y)^{2} + (b x - a y)^{2}$ factorise it

Open in App

Solution

Given, $(a x + b y) ² + (b x - a y) ²$

$= a ² x ² + b ² y ² + 2 a b x y + b ² x ² + a ² y ² - 2 a b x y$ $[∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b, (a - b)^{2} = a^{2} + b^{2} - 2 a b]$

$= a ² x ² + b ² x ² + b ² y ² + a ² y ²$

$= x ² (a ² + b ²) + y ² (a ² + b ²)$

$= (a ² + b ²) (x ² + y ²)$

Hence, factorise of $(a x + b y)^{2} + (b x - a y)^{2}$ is $(a^{2} + b^{2}) (x^{2} + y^{2})$

Suggest Corrections

109

Similar questions

a x + b x + a y + b y

a x^{2} + b y^{2} + b x^{2} + a y^{2}

a^{2} + b c + a b + a c

a x - a y + b x - b y

(i) a x + b x + a y + b y

(i i) a x^{2} + b y^{2} + b x^{2} + a y^{2}

(i i i) a^{2} + b c + a b + a c

(i v) a x - a y + b x - b y

a x^{2} + b x^{2} + a y^{2} + b y^{2}

(a x + b y)^{2} - (b x + a y)^{2}

a x + b x - a y - b y

Join BYJU'S Learning Program