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

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

Evaluate

$$y^{4}-\frac{9}{4}$$

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}. Square \frac{3}{2}.

$$\left(y^{2}\right)^{2}-\frac{9}{4}$$

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

$$y^{4}-\frac{9}{4}$$

Expand

$$y^{4}-\frac{9}{4}$$

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}. Square \frac{3}{2}.

$$\left(y^{2}\right)^{2}-\frac{9}{4}$$

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

$$y^{4}-\frac{9}{4}$$