What is factor (x^2+xy^2)^2-(xy+y^2)^2 ?

The solution to factor (x^2+xy^2)^2-(xy+y^2)^2 is (x^2+xy^2+xy+y^2)(x^2+xy^2-xy-y^2)

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factor (x^2+xy^2)^2-(xy+y^2)^2

factor

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

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

Solution steps

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2} + x y^{2})^{2} - (x y + y^{2})^{2} = ((x^{2} + x y^{2}) + (x y + y^{2})) ((x^{2} + x y^{2}) - (x y + y^{2}))

= ((x^{2} + x y^{2}) + (x y + y^{2})) ((x^{2} + x y^{2}) - (x y + y^{2}))

Simplify

((x^{2} + x y^{2}) + (x y + y^{2})) ((x^{2} + x y^{2}) - (x y + y^{2})) : (x^{2} + x y^{2} + x y + y^{2}) (x^{2} + x y^{2} - x y - y^{2})

= (x^{2} + x y^{2} + x y + y^{2}) (x^{2} + x y^{2} - x y - y^{2})

(x^{- 2})^{2}

32.5 \cdot \frac{1}{71.1} \cdot \frac{4}{4} \cdot 56.11

5^{x^{2}} > 2^{x}

- \frac{2}{3} ln (1 - 9^{\frac{3}{2}}) = 0 + C

4 - x^{2}

What is factor (x^2+xy^2)^2-(xy+y^2)^2 ?
The solution to factor (x^2+xy^2)^2-(xy+y^2)^2 is (x^2+xy^2+xy+y^2)(x^2+xy^2-xy-y^2)