Solve 1(2-3sqrt{2})^2-(-3/5)^-2-1

$$1 ( 2 - 3 \sqrt { 2 } ) ^ { 2 } - ( - \frac { 3 } { 5 } ) ^ { - 2 } - 1$$

Evaluate

$$\frac{164}{9}-12\sqrt{2}\approx 1.251659474$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-3\sqrt{2}\right)^{2}.

$$1\left(4-12\sqrt{2}+9\left(\sqrt{2}\right)^{2}\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

The square of \sqrt{2} is 2.

$$1\left(4-12\sqrt{2}+9\times 2\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Multiply 9 and 2 to get 18.

$$1\left(4-12\sqrt{2}+18\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Add 4 and 18 to get 22.

$$1\left(22-12\sqrt{2}\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Use the distributive property to multiply 1 by 22-12\sqrt{2}.

$$22-12\sqrt{2}-\left(-\frac{3}{5}\right)^{-2}-1$$

Calculate -\frac{3}{5} to the power of -2 and get \frac{25}{9}.

$$22-12\sqrt{2}-\frac{25}{9}-1$$

Subtract \frac{25}{9} from 22 to get \frac{173}{9}.

$$\frac{173}{9}-12\sqrt{2}-1$$

Subtract 1 from \frac{173}{9} to get \frac{164}{9}.

$$\frac{164}{9}-12\sqrt{2}$$

Expand

$$\frac{164}{9} - 12 \sqrt{2} = 1.251659474$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-3\sqrt{2}\right)^{2}.

$$1\left(4-12\sqrt{2}+9\left(\sqrt{2}\right)^{2}\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

The square of \sqrt{2} is 2.

$$1\left(4-12\sqrt{2}+9\times 2\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Multiply 9 and 2 to get 18.

$$1\left(4-12\sqrt{2}+18\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Add 4 and 18 to get 22.

$$1\left(22-12\sqrt{2}\right)-\left(-\frac{3}{5}\right)^{-2}-1$$

Use the distributive property to multiply 1 by 22-12\sqrt{2}.

$$22-12\sqrt{2}-\left(-\frac{3}{5}\right)^{-2}-1$$

Calculate -\frac{3}{5} to the power of -2 and get \frac{25}{9}.

$$22-12\sqrt{2}-\frac{25}{9}-1$$

Subtract \frac{25}{9} from 22 to get \frac{173}{9}.

$$\frac{173}{9}-12\sqrt{2}-1$$

Subtract 1 from \frac{173}{9} to get \frac{164}{9}.

$$\frac{164}{9}-12\sqrt{2}$$