Solve (4y)^2+4y^2+8y^2/(4y+2y)(4y-3y)

$$\frac { ( 4 y ) ^ { 2 } + 4 y ^ { 2 } + 8 y ^ { 2 } } { ( 4 y + 2 y ) ( 4 y - 3 y ) }$$

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Expand \left(4y\right)^{2}.

$$\frac{4^{2}y^{2}+4y^{2}+8y^{2}}{\left(4y+2y\right)\left(4y-3y\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16y^{2}+4y^{2}+8y^{2}}{\left(4y+2y\right)\left(4y-3y\right)}$$

Combine 16y^{2} and 4y^{2} to get 20y^{2}.

$$\frac{20y^{2}+8y^{2}}{\left(4y+2y\right)\left(4y-3y\right)}$$

Combine 20y^{2} and 8y^{2} to get 28y^{2}.

$$\frac{28y^{2}}{\left(4y+2y\right)\left(4y-3y\right)}$$

Combine 4y and 2y to get 6y.

$$\frac{28y^{2}}{6y\left(4y-3y\right)}$$

Combine 4y and -3y to get y.

$$\frac{28y^{2}}{6yy}$$

Multiply y and y to get y^{2}.

$$\frac{28y^{2}}{6y^{2}}$$

Cancel out 2y^{2} in both numerator and denominator.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$