Solve (y^2+7/3)(y^2+7/3)

$$( y ^ { 2 } + \frac { 7 } { 3 } ) ( y ^ { 2 } + \frac { 7 } { 3 } )$$

Evaluate

$$\frac{\left(3y^{2}+7\right)^{2}}{9}$$

Solution Steps

Multiply y^{2}+\frac{7}{3} and y^{2}+\frac{7}{3} to get \left(y^{2}+\frac{7}{3}\right)^{2}.

$$\left(y^{2}+\frac{7}{3}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y^{2}+\frac{7}{3}\right)^{2}.

$$\left(y^{2}\right)^{2}+\frac{14}{3}y^{2}+\frac{49}{9}$$

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

$$y^{4}+\frac{14}{3}y^{2}+\frac{49}{9}$$

Expand

$$y^{4}+\frac{14y^{2}}{3}+\frac{49}{9}$$

Solution Steps

Multiply y^{2}+\frac{7}{3} and y^{2}+\frac{7}{3} to get \left(y^{2}+\frac{7}{3}\right)^{2}.

$$\left(y^{2}+\frac{7}{3}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y^{2}+\frac{7}{3}\right)^{2}.

$$\left(y^{2}\right)^{2}+\frac{14}{3}y^{2}+\frac{49}{9}$$

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

$$y^{4}+\frac{14}{3}y^{2}+\frac{49}{9}$$