What is expand (ax^2+by^2)^2 ?

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

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expand (ax^2+by^2)^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{7 - 7}{7}

63 x - 28 x

(\frac{4}{9})^{\frac{- 1}{2}}

5 x^{2} - 10 x^{3}

(2 t - 1) (t + 5)

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