Solve (15+x)^2+(15^2-x^2)^2

$$( 15 + x ) ^ { 2 } + ( 15 ^ { 2 } - x ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\left(x+15\right)^{2}\left(x^{2}-30x+226\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(15+x\right)^{2}.

$$225+30x+x^{2}+\left(15^{2}-x^{2}\right)^{2}$$

Calculate 15 to the power of 2 and get 225.

$$225+30x+x^{2}+\left(225-x^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(225-x^{2}\right)^{2}.

$$225+30x+x^{2}[phone]x^{2}+\left(x^{2}\right)^{2}$$

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

$$225+30x+x^{2}[phone]x^{2}+x^{4}$$

Add 225 and 50625 to get 50850.

$$50850+30x+x^{2}-450x^{2}+x^{4}$$

Combine x^{2} and -450x^{2} to get -449x^{2}.

$$50850+30x-449x^{2}+x^{4}$$

Expand

$$x^{4}-449x^{2}+30x+50850$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(15+x\right)^{2}.

$$225+30x+x^{2}+\left(15^{2}-x^{2}\right)^{2}$$

Calculate 15 to the power of 2 and get 225.

$$225+30x+x^{2}+\left(225-x^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(225-x^{2}\right)^{2}.

$$225+30x+x^{2}[phone]x^{2}+\left(x^{2}\right)^{2}$$

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

$$225+30x+x^{2}[phone]x^{2}+x^{4}$$

Add 225 and 50625 to get 50850.

$$50850+30x+x^{2}-450x^{2}+x^{4}$$

Combine x^{2} and -450x^{2} to get -449x^{2}.

$$50850+30x-449x^{2}+x^{4}$$