Solve left(3x^2+xright)^2

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

Evaluate

$$\left(x\left(3x+1\right)\right)^{2}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}+6x^{2}x+x^{2}$$

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

$$9x^{4}+6x^{2}x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$9x^{4}+6x^{3}+x^{2}$$

Expand

$$9x^{4}+6x^{3}+x^{2}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}+6x^{2}x+x^{2}$$

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

$$9x^{4}+6x^{2}x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$9x^{4}+6x^{3}+x^{2}$$