Solve [(5*9^2)-(90+Y^2)]^2

$$[ ( 5 \times 9 ^ { 2 } ) - ( 90 + Y ^ { 2 } ) ] ^ { 2 }$$

Evaluate

$$\left(315-Y^{2}\right)^{2}$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\left(5\times 81-\left(90+Y^{2}\right)\right)^{2}$$

Multiply 5 and 81 to get 405.

$$\left(405-\left(90+Y^{2}\right)\right)^{2}$$

To find the opposite of 90+Y^{2}, find the opposite of each term.

$$\left(405-90-Y^{2}\right)^{2}$$

Subtract 90 from 405 to get 315.

$$\left(315-Y^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(315-Y^{2}\right)^{2}.

$$99225-630Y^{2}+\left(Y^{2}\right)^{2}$$

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

$$99225-630Y^{2}+Y^{4}$$

Expand

$$Y^{4}-630Y^{2}+99225$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\left(5\times 81-\left(90+Y^{2}\right)\right)^{2}$$

Multiply 5 and 81 to get 405.

$$\left(405-\left(90+Y^{2}\right)\right)^{2}$$

To find the opposite of 90+Y^{2}, find the opposite of each term.

$$\left(405-90-Y^{2}\right)^{2}$$

Subtract 90 from 405 to get 315.

$$\left(315-Y^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(315-Y^{2}\right)^{2}.

$$99225-630Y^{2}+\left(Y^{2}\right)^{2}$$

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

$$99225-630Y^{2}+Y^{4}$$