What is expand (a^2x+by^2)^2 ?

The solution to expand (a^2x+by^2)^2 is a^4x^2+2bxa^2y^2+b^2y^4

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expand (a^2x+by^2)^2

expand

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

a^{4} x^{2} + 2 b x a^{2} y^{2} + b^{2} y^{4}

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

(a^{2} x)^{2} + 2 a^{2} x b y^{2} + (b y^{2})^{2} : a^{4} x^{2} + 2 b x a^{2} y^{2} + b^{2} y^{4}

= a^{4} x^{2} + 2 b x a^{2} y^{2} + b^{2} y^{4}

\frac{4}{24}

\frac{3 x}{6 x ^{2}}

\frac{10}{30}

(x - 4) (x + 5)

What is expand (a^2x+by^2)^2 ?
The solution to expand (a^2x+by^2)^2 is a^4x^2+2bxa^2y^2+b^2y^4