Solve quadf(x)=(x^2+25)^3

$$\quad f ( x ) = ( x ^ { 2 } + 25 ) ^ { 3 }$$

Evaluate

$$\left(x^{2}+25\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{2}+25\right)^{3}.

$$\left(x^{2}\right)^{3}+75\left(x^{2}\right)^{2}+1875x^{2}+15625$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$x^{6}+75\left(x^{2}\right)^{2}+1875x^{2}+15625$$

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

$$x^{6}+75x^{4}+1875x^{2}+15625$$

Expand

$$x^{6}+75x^{4}+1875x^{2}+15625$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x^{2}+25\right)^{3}.

$$\left(x^{2}\right)^{3}+75\left(x^{2}\right)^{2}+1875x^{2}+15625$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$x^{6}+75\left(x^{2}\right)^{2}+1875x^{2}+15625$$

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

$$x^{6}+75x^{4}+1875x^{2}+15625$$