Solve (3+3z)^2+5z(4+4z)

$$( 3 + 3 z ) ^ { 2 } + 5 z ( 4 + 4 z )$$

Evaluate

$$\left(z+1\right)\left(29z+9\right)$$

Solution Steps

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

$$9+18z+9z^{2}+5z\left(4+4z\right)$$

Use the distributive property to multiply 5z by 4+4z.

$$9+18z+9z^{2}+20z+20z^{2}$$

Combine 18z and 20z to get 38z.

$$9+38z+9z^{2}+20z^{2}$$

Combine 9z^{2} and 20z^{2} to get 29z^{2}.

$$9+38z+29z^{2}$$

Expand

$$29z^{2}+38z+9$$

Solution Steps

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

$$9+18z+9z^{2}+5z\left(4+4z\right)$$

Use the distributive property to multiply 5z by 4+4z.

$$9+18z+9z^{2}+20z+20z^{2}$$

Combine 18z and 20z to get 38z.

$$9+38z+9z^{2}+20z^{2}$$

Combine 9z^{2} and 20z^{2} to get 29z^{2}.

$$9+38z+29z^{2}$$