Solve [(1+x)(1-2x)^2]

$$[ ( 1 + x ) ( 1 - 2 x ) ^ { 2 } ]$$

Evaluate

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

Solution Steps

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

$$\left(1+x\right)\left(1-4x+4x^{2}\right)$$

Use the distributive property to multiply 1+x by 1-4x+4x^{2} and combine like terms.

$$1-3x+4x^{3}$$

Expand

$$4x^{3}-3x+1$$

Solution Steps

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

$$\left(1+x\right)\left(1-4x+4x^{2}\right)$$

Use the distributive property to multiply 1+x by 1-4x+4x^{2} and combine like terms.

$$1-3x+4x^{3}$$