Solve (1+x)^2(1+2x)^2

$$( 1 + x ) ^ { 2 } ( 1 + 2 x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$1+6x+13x^{2}+12x^{3}+4x^{4}$$

Expand

$$4x^{4}+12x^{3}+13x^{2}+6x+1$$

Solution Steps

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

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

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

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

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

$$1+6x+13x^{2}+12x^{3}+4x^{4}$$