Solve (2x+3y)(2x-3y)(4(x)^(2)+9(y)^(2))(16(x)^(4)+81(y)^(4)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2x+3y)(2x-3y)(4 { x }^{ 2 } +9 { y }^{ 2 } )(16 { x }^{ 4 } +81 { y }^{ 4 } )$$

Evaluate

$256x^{8}-6561y^{8}$

Solution Steps

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

$$\left(4x^{2}-9y^{2}\right)\left(4x^{2}+9y^{2}\right)\left(16x^{4}+81y^{4}\right)$$

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

$$\left(16x^{4}-81y^{4}\right)\left(16x^{4}+81y^{4}\right)$$

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\left(16x^{4}\right)^{2}-\left(81y^{4}\right)^{2}$$

Expand $\left(16x^{4}\right)^{2}$.

$$16^{2}\left(x^{4}\right)^{2}-\left(81y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$16^{2}x^{8}-\left(81y^{4}\right)^{2}$$

Calculate $16$ to the power of $2$ and get $256$.

$$256x^{8}-\left(81y^{4}\right)^{2}$$

Expand $\left(81y^{4}\right)^{2}$.

$$256x^{8}-81^{2}\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$256x^{8}-81^{2}y^{8}$$

Calculate $81$ to the power of $2$ and get $6561$.

$$256x^{8}-6561y^{8}$$

Expand

$256x^{8}-6561y^{8}$

Solution Steps

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

$$\left(4x^{2}-9y^{2}\right)\left(4x^{2}+9y^{2}\right)\left(16x^{4}+81y^{4}\right)$$

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

$$\left(16x^{4}-81y^{4}\right)\left(16x^{4}+81y^{4}\right)$$

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\left(16x^{4}\right)^{2}-\left(81y^{4}\right)^{2}$$

Expand $\left(16x^{4}\right)^{2}$.

$$16^{2}\left(x^{4}\right)^{2}-\left(81y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$16^{2}x^{8}-\left(81y^{4}\right)^{2}$$

Calculate $16$ to the power of $2$ and get $256$.

$$256x^{8}-\left(81y^{4}\right)^{2}$$

Expand $\left(81y^{4}\right)^{2}$.

$$256x^{8}-81^{2}\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$256x^{8}-81^{2}y^{8}$$

Calculate $81$ to the power of $2$ and get $6561$.

$$256x^{8}-6561y^{8}$$