Solve 8(1+2b)^2(2+b)

$$8 ( 1 + 2 b ) ^ { 2 } ( 2 + b )$$

Evaluate

$$8\left(b+2\right)\left(2b+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(1+2b\right)^{2}.

$$8\left(1+4b+4b^{2}\right)\left(2+b\right)$$

Use the distributive property to multiply 8 by 1+4b+4b^{2}.

$$\left(8+32b+32b^{2}\right)\left(2+b\right)$$

Use the distributive property to multiply 8+32b+32b^{2} by 2+b and combine like terms.

$$16+72b+96b^{2}+32b^{3}$$

Expand

$$32b^{3}+96b^{2}+72b+16$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(1+2b\right)^{2}.

$$8\left(1+4b+4b^{2}\right)\left(2+b\right)$$

Use the distributive property to multiply 8 by 1+4b+4b^{2}.

$$\left(8+32b+32b^{2}\right)\left(2+b\right)$$

Use the distributive property to multiply 8+32b+32b^{2} by 2+b and combine like terms.

$$16+72b+96b^{2}+32b^{3}$$