Solve (8x^3+2x)^2

$$( 8 x ^ { 3 } + 2 x ) ^ { 2 }$$

Evaluate

$$4\left(4x^{3}+x\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{3}+2x\right)^{2}.

$$64\left(x^{3}\right)^{2}+32x^{3}x+4x^{2}$$

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

$$64x^{6}+32x^{3}x+4x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$64x^{6}+32x^{4}+4x^{2}$$

Expand

$$64x^{6}+32x^{4}+4x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{3}+2x\right)^{2}.

$$64\left(x^{3}\right)^{2}+32x^{3}x+4x^{2}$$

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

$$64x^{6}+32x^{3}x+4x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$64x^{6}+32x^{4}+4x^{2}$$