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

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

Evaluate

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

Solution Steps

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

$$8x^{3}+36x^{2}x^{2}+54x\left(x^{2}\right)^{2}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x\left(x^{2}\right)^{2}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54xx^{4}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x^{5}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x^{5}+27x^{6}$$

Expand

$$27x^{6}+54x^{5}+36x^{4}+8x^{3}$$

Solution Steps

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

$$8x^{3}+36x^{2}x^{2}+54x\left(x^{2}\right)^{2}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x\left(x^{2}\right)^{2}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54xx^{4}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x^{5}+27\left(x^{2}\right)^{3}$$

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

$$8x^{3}+36x^{4}+54x^{5}+27x^{6}$$