Solve y=(2x^4+6x)^3

$$y = ( 2 x ^ { 4 } + 6 x ) ^ { 3 }$$

Solve for y

$$y=8\left(x\left(x^{3}+3\right)\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x^{4}+6x\right)^{3}.

$$y=8\left(x^{4}\right)^{3}+72\left(x^{4}\right)^{2}x+216x^{4}x^{2}+216x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$y=8x^{12}+72\left(x^{4}\right)^{2}x+216x^{4}x^{2}+216x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$y=8x^{12}+72x^{8}x+216x^{4}x^{2}+216x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$y=8x^{12}+72x^{9}+216x^{4}x^{2}+216x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$y=8x^{12}+72x^{9}+216x^{6}+216x^{3}$$