Solve 1440(1+x)^2-100

$$1440 ( 1 + x ) ^ { 2 } - 100$$

Evaluate

$$1440\left(x+1\right)^{2}-100$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.

$$1440\left(1+2x+x^{2}\right)-100$$

Use the distributive property to multiply 1440 by 1+2x+x^{2}.

$$1440+2880x+1440x^{2}-100$$

Subtract 100 from 1440 to get 1340.

$$1340+2880x+1440x^{2}$$

Expand

$$1440x^{2}+2880x+1340$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.

$$1440\left(1+2x+x^{2}\right)-100$$

Use the distributive property to multiply 1440 by 1+2x+x^{2}.

$$1440+2880x+1440x^{2}-100$$

Subtract 100 from 1440 to get 1340.

$$1340+2880x+1440x^{2}$$