Solve (3x^2+1/2y)(3x^2-1/2y)=

$$( 3 x ^ { 2 } + \frac { 1 } { 2 } y ) ( 3 x ^ { 2 } - \frac { 1 } { 2 } y ) =$$

Evaluate

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

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}.

$$\left(3x^{2}\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$3^{2}\left(x^{2}\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$3^{2}x^{4}-\left(\frac{1}{2}y\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(\frac{1}{2}y\right)^{2}$$

Expand \left(\frac{1}{2}y\right)^{2}.

$$9x^{4}-\left(\frac{1}{2}\right)^{2}y^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$9x^{4}-\frac{1}{4}y^{2}$$

Expand

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

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}.

$$\left(3x^{2}\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$3^{2}\left(x^{2}\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$3^{2}x^{4}-\left(\frac{1}{2}y\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(\frac{1}{2}y\right)^{2}$$

Expand \left(\frac{1}{2}y\right)^{2}.

$$9x^{4}-\left(\frac{1}{2}\right)^{2}y^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$9x^{4}-\frac{1}{4}y^{2}$$