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

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

Evaluate

$72xy^{4}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(9x+2y^{4}\right)^{2}$.

$$81x^{2}+36xy^{4}+4\left(y^{4}\right)^{2}-\left(2y^{4}-9x\right)^{2}$$

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

$$81x^{2}+36xy^{4}+4y^{8}-\left(2y^{4}-9x\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2y^{4}-9x\right)^{2}$.

$$81x^{2}+36xy^{4}+4y^{8}-\left(4\left(y^{4}\right)^{2}-36y^{4}x+81x^{2}\right)$$

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

$$81x^{2}+36xy^{4}+4y^{8}-\left(4y^{8}-36y^{4}x+81x^{2}\right)$$

To find the opposite of $4y^{8}-36y^{4}x+81x^{2}$, find the opposite of each term.

$$81x^{2}+36xy^{4}+4y^{8}-4y^{8}+36y^{4}x-81x^{2}$$

Combine $4y^{8}$ and $-4y^{8}$ to get $0$.

$$81x^{2}+36xy^{4}+36y^{4}x-81x^{2}$$

Combine $36xy^{4}$ and $36y^{4}x$ to get $72xy^{4}$.

$$81x^{2}+72xy^{4}-81x^{2}$$

Combine $81x^{2}$ and $-81x^{2}$ to get $0$.

$$72xy^{4}$$

Expand

$72xy^{4}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(9x+2y^{4}\right)^{2}$.

$$81x^{2}+36xy^{4}+4\left(y^{4}\right)^{2}-\left(2y^{4}-9x\right)^{2}$$

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

$$81x^{2}+36xy^{4}+4y^{8}-\left(2y^{4}-9x\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2y^{4}-9x\right)^{2}$.

$$81x^{2}+36xy^{4}+4y^{8}-\left(4\left(y^{4}\right)^{2}-36y^{4}x+81x^{2}\right)$$

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

$$81x^{2}+36xy^{4}+4y^{8}-\left(4y^{8}-36y^{4}x+81x^{2}\right)$$

To find the opposite of $4y^{8}-36y^{4}x+81x^{2}$, find the opposite of each term.

$$81x^{2}+36xy^{4}+4y^{8}-4y^{8}+36y^{4}x-81x^{2}$$

Combine $4y^{8}$ and $-4y^{8}$ to get $0$.

$$81x^{2}+36xy^{4}+36y^{4}x-81x^{2}$$

Combine $36xy^{4}$ and $36y^{4}x$ to get $72xy^{4}$.

$$81x^{2}+72xy^{4}-81x^{2}$$

Combine $81x^{2}$ and $-81x^{2}$ to get $0$.

$$72xy^{4}$$