Solve -3^2quadtext{II}47^2-3^4:9

$$- 3 ^ { 2 } \quad \text { II } 47 ^ { 2 } - 3 ^ { 4 } : 9$$

Evaluate

$$-19881I^{2}-9$$

Solution Steps

Multiply I and I to get I^{2}.

$$\left(-3^{2}\right)I^{2}\times 47^{2}-\frac{3^{4}}{9}$$

Calculate 3 to the power of 2 and get 9.

$$-9I^{2}\times 47^{2}-\frac{3^{4}}{9}$$

Calculate 47 to the power of 2 and get 2209.

$$-9I^{2}\times 2209-\frac{3^{4}}{9}$$

Multiply -9 and 2209 to get -19881.

$$-19881I^{2}-\frac{3^{4}}{9}$$

Calculate 3 to the power of 4 and get 81.

$$-19881I^{2}-\frac{81}{9}$$

Divide 81 by 9 to get 9.

$$-19881I^{2}-9$$

Factor

$$9\left(-2209I^{2}-1\right)$$

Solution Steps

Factor out 9. Polynomial -2209I^{2}-1 is not factored since it does not have any rational roots.

$$9\left(-2209II-1\right)$$