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

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

Evaluate

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

Solution Steps

Combine x and 2x to get 3x.

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

Expand \left(2x\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$27x^{3}+108x^{2}x^{2}+144x\left(x^{2}\right)^{2}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144x\left(x^{2}\right)^{2}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144xx^{4}+64\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$27x^{3}+108x^{4}+144x^{5}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144x^{5}+64x^{6}$$

Expand

$$64x^{6}+144x^{5}+108x^{4}+27x^{3}$$

Solution Steps

Combine x and 2x to get 3x.

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

Expand \left(2x\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$27x^{3}+108x^{2}x^{2}+144x\left(x^{2}\right)^{2}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144x\left(x^{2}\right)^{2}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144xx^{4}+64\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$27x^{3}+108x^{4}+144x^{5}+64\left(x^{2}\right)^{3}$$

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

$$27x^{3}+108x^{4}+144x^{5}+64x^{6}$$