Solve (-0,2x^2+2/3x)^2

$$( - 0,2 x ^ { 2 } + \frac { 2 } { 3 } x ) ^ { 2 }$$

Evaluate

$$\frac{\left(x\left(-\frac{3x}{5}+2\right)\right)^{2}}{9}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-0,2x^{2}+\frac{2}{3}x\right)^{2}.

$$0,04\left(x^{2}\right)^{2}-\frac{4}{15}x^{2}x+\frac{4}{9}x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$0,04x^{4}-\frac{4}{15}x^{2}x+\frac{4}{9}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$0,04x^{4}-\frac{4}{15}x^{3}+\frac{4}{9}x^{2}$$

Expand

$$\frac{x^{4}}{25}-\frac{4x^{3}}{15}+\frac{4x^{2}}{9}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-0,2x^{2}+\frac{2}{3}x\right)^{2}.

$$0,04\left(x^{2}\right)^{2}-\frac{4}{15}x^{2}x+\frac{4}{9}x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$0,04x^{4}-\frac{4}{15}x^{2}x+\frac{4}{9}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$0,04x^{4}-\frac{4}{15}x^{3}+\frac{4}{9}x^{2}$$