Solve (3y^3+2y^2)^3

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

Evaluate

$$\left(3y+2\right)^{3}y^{6}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$27y^{9}+54\left(y^{3}\right)^{2}y^{2}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{6}y^{2}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$27y^{9}+54y^{8}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{8}+36y^{3}y^{4}+8\left(y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$27y^{9}+54y^{8}+36y^{7}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{8}+36y^{7}+8y^{6}$$

Expand

$$27y^{9}+54y^{8}+36y^{7}+8y^{6}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$27y^{9}+54\left(y^{3}\right)^{2}y^{2}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{6}y^{2}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$27y^{9}+54y^{8}+36y^{3}\left(y^{2}\right)^{2}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{8}+36y^{3}y^{4}+8\left(y^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$27y^{9}+54y^{8}+36y^{7}+8\left(y^{2}\right)^{3}$$

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

$$27y^{9}+54y^{8}+36y^{7}+8y^{6}$$