Solve (3x^2+70)^2

$$( 3 x ^ { 2 } + 70 ) ^ { 2 }$$

Expand

$$9x^{4}+420x^{2}+4900$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x^{2}+70\right)^{2}.

$$9\left(x^{2}\right)^{2}+420x^{2}+4900$$

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

$$9x^{4}+420x^{2}+4900$$

Evaluate

$$\left(3x^{2}+70\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x^{2}+70\right)^{2}.

$$9\left(x^{2}\right)^{2}+420x^{2}+4900$$

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

$$9x^{4}+420x^{2}+4900$$