Solve 3b^4+18b^3+27b^2

$$3 b ^ { 4 } + 18 b ^ { 3 } + 27 b ^ { 2 }$$

Factor

$$3b^{2}\left(b+3\right)^{2}$$

Solution Steps

Factor out 3.

$$3\left(b^{4}+6b^{3}+9b^{2}\right)$$

Consider b^{4}+6b^{3}+9b^{2}. Factor out b^{2}.

$$b^{2}\left(b^{2}+6b+9\right)$$

Consider b^{2}+6b+9. Use the perfect square formula, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, where p=b and q=3.

$$\left(b+3\right)^{2}$$

Rewrite the complete factored expression.

$$3b^{2}\left(b+3\right)^{2}$$

Evaluate

$$3\left(b\left(b+3\right)\right)^{2}$$