Solve (x^2+3/2y)(3/2y-x^2)(9/4y^2+x^4)

$$( x ^ { 2 } + \frac { 3 } { 2 } y ) ( \frac { 3 } { 2 } y - x ^ { 2 } ) ( \frac { 9 } { 4 } y ^ { 2 } + x ^ { 4 } )$$

Evaluate

$$-x^{8}+\frac{81y^{4}}{16}$$

Solution Steps

Use the distributive property to multiply x^{2}+\frac{3}{2}y by \frac{3}{2}y-x^{2} and combine like terms.

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

Use the distributive property to multiply -x^{4}+\frac{9}{4}y^{2} by \frac{9}{4}y^{2}+x^{4} and combine like terms.

$$-x^{8}+\frac{81}{16}y^{4}$$

Expand

$$-x^{8}+\frac{81y^{4}}{16}$$

Solution Steps

Use the distributive property to multiply x^{2}+\frac{3}{2}y by \frac{3}{2}y-x^{2} and combine like terms.

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

Use the distributive property to multiply -x^{4}+\frac{9}{4}y^{2} by \frac{9}{4}y^{2}+x^{4} and combine like terms.

$$-x^{8}+\frac{81}{16}y^{4}$$