What is expand (8x^2+4y)|x^2+y^2=1| ?

The solution to expand (8x^2+4y)|x^2+y^2=1| is 8x^2|x^2+1=y^2|+4y|x^2+1=y^2|

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expand (8x^2+4y)|x^2+y^2=1|

expand

(8 x^{2} + 4 y) x^{2} + y^{2} = 1

8 x^{2} x^{2} + 1 = y^{2} + 4 y x^{2} + 1 = y^{2}

Solution steps

(8 x^{2} + 4 y) x^{2} + y^{2} = 1

= x^{2} + 1 = y^{2} (8 x^{2} + 4 y)

Apply the distributive law:

a (b + c) = ab + a c

a = x^{2} + y^{2} = 1, b = 8 x^{2}, c = 4 y

= x^{2} + y^{2} = 1 \cdot 8 x^{2} + x^{2} + y^{2} = 1 \cdot 4 y

= 8 x^{2} x^{2} + 1 = y^{2} + 4 y x^{2} + 1 = y^{2}

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What is expand (8x^2+4y)|x^2+y^2=1| ?
The solution to expand (8x^2+4y)|x^2+y^2=1| is 8x^2|x^2+1=y^2|+4y|x^2+1=y^2|