Solve 2Ax^2+4ABx+2AB^2

$$2 A x ^ { 2 } + 4 A B x + 2 A B ^ { 2 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(Ax^{2}+2ABx+AB^{2}\right)$$

Consider Ax^{2}+2ABx+AB^{2}. Factor out A.

$$A\left(x^{2}+2Bx+B^{2}\right)$$

Consider x^{2}+2Bx+B^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=B.

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

Rewrite the complete factored expression.

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

Evaluate

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