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

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

Evaluate

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

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$\left(-\frac{3}{2}x\right)^{2}-x^{4}$$

Expand \left(-\frac{3}{2}x\right)^{2}.

$$\left(-\frac{3}{2}\right)^{2}x^{2}-x^{4}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}x^{2}-x^{4}$$

Expand

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

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$\left(-\frac{3}{2}x\right)^{2}-x^{4}$$

Expand \left(-\frac{3}{2}x\right)^{2}.

$$\left(-\frac{3}{2}\right)^{2}x^{2}-x^{4}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}x^{2}-x^{4}$$