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

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

Evaluate

$$8\left(x\left(x+1\right)\right)^{3}$$

Solution Steps

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

$$8\left(x^{2}\right)^{3}+24\left(x^{2}\right)^{2}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24\left(x^{2}\right)^{2}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{4}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{5}+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{5}+24x^{4}+8x^{3}$$

Expand

$$8x^{6}+24x^{5}+24x^{4}+8x^{3}$$

Solution Steps

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

$$8\left(x^{2}\right)^{3}+24\left(x^{2}\right)^{2}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24\left(x^{2}\right)^{2}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{4}x+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{5}+24x^{2}x^{2}+8x^{3}$$

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

$$8x^{6}+24x^{5}+24x^{4}+8x^{3}$$