What is (sqrt(5)*y^2-sqrt(10)*z^2)^2 ?

The solution to (sqrt(5)*y^2-sqrt(10)*z^2)^2 is 5y^4-10sqrt(2)y^2z^2+10z^4

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simplify (sqrt(5)y^2-sqrt(10)z^2)^2

simplify

(5 \cdot y^{2} - 10 \cdot z^{2})^{2}

5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}

Solution steps

(5 y^{2} - 10 z^{2})^{2}

Apply Perfect Square Formula:

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

(5 y^{2} - 10 z^{2})^{2} = (5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2}

= (5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2}

Simplify

(5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2} : 5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}

= 5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}

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(a - 1) \cdot (a + 1) \cdot (a^{2} + a + 1) \cdot (a^{2} - a + 1)

2130829 k^{1} - 18041807671

3 sin^{2} (a) + 3 cos^{2} (a)

What is (sqrt(5)*y^2-sqrt(10)*z^2)^2 ?
The solution to (sqrt(5)*y^2-sqrt(10)*z^2)^2 is 5y^4-10sqrt(2)y^2z^2+10z^4