Solve z(50+z)^2

$$z ( 50 + z ) ^ { 2 }$$

Evaluate

$$z\left(z+50\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(50+z\right)^{2}.

$$z\left(2500+100z+z^{2}\right)$$

Use the distributive property to multiply z by 2500+100z+z^{2}.

$$2500z+100z^{2}+z^{3}$$

Expand

$$z^{3}+100z^{2}+2500z$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(50+z\right)^{2}.

$$z\left(2500+100z+z^{2}\right)$$

Use the distributive property to multiply z by 2500+100z+z^{2}.

$$2500z+100z^{2}+z^{3}$$