Solve (2x+3y)(2x-3y)(4x^2+6xy+9y^2)(4x^2-6xy+9y^2)

$$( 2 x + 3 y ) ( 2 x - 3 y ) ( 4 x ^ { 2 } + 6 x y + 9 y ^ { 2 } ) ( 4 x ^ { 2 } - 6 x y + 9 y ^ { 2 } )$$

Evaluate

$$\left(4x^{2}-9y^{2}\right)\left(-36\left(xy\right)^{2}+\left(4x^{2}+9y^{2}\right)^{2}\right)$$

Solution Steps

Use the distributive property to multiply 2x+3y by 2x-3y and combine like terms.

$$\left(4x^{2}-9y^{2}\right)\left(4x^{2}+6xy+9y^{2}\right)\left(4x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 4x^{2}-9y^{2} by 4x^{2}+6xy+9y^{2} and combine like terms.

$$\left(16x^{4}+24x^{3}y-54y^{3}x-81y^{4}\right)\left(4x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 16x^{4}+24x^{3}y-54y^{3}x-81y^{4} by 4x^{2}-6xy+9y^{2} and combine like terms.

$$64x^{6}-729y^{6}$$

Expand

$$64x^{6}-729y^{6}$$

Solution Steps

Use the distributive property to multiply 2x+3y by 2x-3y and combine like terms.

$$\left(4x^{2}-9y^{2}\right)\left(4x^{2}+6xy+9y^{2}\right)\left(4x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 4x^{2}-9y^{2} by 4x^{2}+6xy+9y^{2} and combine like terms.

$$\left(16x^{4}+24x^{3}y-54y^{3}x-81y^{4}\right)\left(4x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 16x^{4}+24x^{3}y-54y^{3}x-81y^{4} by 4x^{2}-6xy+9y^{2} and combine like terms.

$$64x^{6}-729y^{6}$$