Solve 4t^2+(18-2t^2)^2

$$4 t ^ { 2 } + ( 18 - 2 t ^ { 2 } ) ^ { 2 }$$

Evaluate

$$4\left(t^{4}-17t^{2}+81\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(18-2t^{2}\right)^{2}.

$$4t^{2}+324-72t^{2}+4\left(t^{2}\right)^{2}$$

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

$$4t^{2}+324-72t^{2}+4t^{4}$$

Combine 4t^{2} and -72t^{2} to get -68t^{2}.

$$-68t^{2}+324+4t^{4}$$

Expand

$$4t^{4}-68t^{2}+324$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(18-2t^{2}\right)^{2}.

$$4t^{2}+324-72t^{2}+4\left(t^{2}\right)^{2}$$

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

$$4t^{2}+324-72t^{2}+4t^{4}$$

Combine 4t^{2} and -72t^{2} to get -68t^{2}.

$$-68t^{2}+324+4t^{4}$$