What is (1/2 y^2-3)^2 ?

The solution to (1/2 y^2-3)^2 is (y^4)/4-3y^2+9

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simplify (1/2 y^2-3)^2

simplify

(\frac{1}{2} y^{2} - 3)^{2}

\frac{y ^{4}}{4} - 3 y^{2} + 9

Solution steps

(\frac{1}{2} y^{2} - 3)^{2}

\frac{1}{2} y^{2} = \frac{y ^{2}}{2}

= (\frac{y ^{2}}{2} - 3)^{2}

Apply Perfect Square Formula:

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

a = \frac{y ^{2}}{2}, b = 3

= (\frac{y ^{2}}{2})^{2} - 2 \cdot \frac{y ^{2}}{2} \cdot 3 + 3^{2}

Simplify

(\frac{y ^{2}}{2})^{2} - 2 \cdot \frac{y ^{2}}{2} \cdot 3 + 3^{2} : \frac{y ^{4}}{4} - 3 y^{2} + 9

= \frac{y ^{4}}{4} - 3 y^{2} + 9

10 98 x^{4} + 5 x^{2} 128

\frac{1500}{0}

6 7 \cdot (1) + 9

- \frac{3}{5} - \frac{1}{2}

\frac{28}{3}