Solve 36a^2-(b^2+9)^2=

$$36 a ^ { 2 } - ( b ^ { 2 } + 9 ) ^ { 2 } =$$

Evaluate

$$-\left(b^{2}+9\right)^{2}+36a^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b^{2}+9\right)^{2}.

$$36a^{2}-\left(\left(b^{2}\right)^{2}+18b^{2}+81\right)$$

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

$$36a^{2}-\left(b^{4}+18b^{2}+81\right)$$

To find the opposite of b^{4}+18b^{2}+81, find the opposite of each term.

$$36a^{2}-b^{4}-18b^{2}-81$$

Expand

$$36a^{2}-b^{4}-18b^{2}-81$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b^{2}+9\right)^{2}.

$$36a^{2}-\left(\left(b^{2}\right)^{2}+18b^{2}+81\right)$$

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

$$36a^{2}-\left(b^{4}+18b^{2}+81\right)$$

To find the opposite of b^{4}+18b^{2}+81, find the opposite of each term.

$$36a^{2}-b^{4}-18b^{2}-81$$