Solve a^3+ab^2+4a+2a^2b-4a^2-4ab

$$a ^ { 3 } + a b ^ { 2 } + 4 a + 2 a ^ { 2 } b - 4 a ^ { 2 } - 4 a b$$

Factor

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

Solution Steps

Factor out a.

$$a\left(a^{2}+b^{2}+4+2ab-4a-4b\right)$$

Consider a^{2}+b^{2}+4+2ab-4a-4b. Use the perfect square formula, p^{2}+q^{2}+r^{2}+2pq+2pr+2qr=\left(p+q+r\right)^{2}, where p=a, q=b and r=-2.

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

Rewrite the complete factored expression.

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

Evaluate

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