Solve {(2x+3y)(2x-3y)}(4(x)^(2)+9(y)^(2)) | 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

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

Evaluate

$16x^{4}-81y^{4}$

Solution Steps

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

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

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

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

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

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

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

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

Calculate $4$ to the power of $2$ and get $16$.

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

Expand $\left(9y^{2}\right)^{2}$.

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

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

$$16x^{4}-9^{2}y^{4}$$

Calculate $9$ to the power of $2$ and get $81$.

$$16x^{4}-81y^{4}$$

Expand

$16x^{4}-81y^{4}$

Solution Steps

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

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

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

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

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

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

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

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

Calculate $4$ to the power of $2$ and get $16$.

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

Expand $\left(9y^{2}\right)^{2}$.

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

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

$$16x^{4}-9^{2}y^{4}$$

Calculate $9$ to the power of $2$ and get $81$.

$$16x^{4}-81y^{4}$$