Solve sqrt{2}left(2-xright)^2+12sqrt{2}

$$\sqrt{ 2 } { \left(2-x \right) }^{ 2 } +12 \sqrt{ 2 }$$

Evaluate

$$\sqrt{2}\left(x^{2}-4x+16\right)$$

Solution Steps

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

$$\sqrt{2}\left(4-4x+x^{2}\right)+12\sqrt{2}$$

Use the distributive property to multiply \sqrt{2} by 4-4x+x^{2}.

$$4\sqrt{2}-4\sqrt{2}x+\sqrt{2}x^{2}+12\sqrt{2}$$

Combine 4\sqrt{2} and 12\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}-4\sqrt{2}x+\sqrt{2}x^{2}$$

Factor

$$\sqrt{2}\left(x^{2}-4x+16\right)$$

Solution Steps

Factor out common term \sqrt{2} by using distributive property.

$$\sqrt{2}\left(\left(2-x\right)^{2}+12\right)$$

Consider \left(2-x\right)^{2}+12. Simplify.

$$x^{2}-4x+16$$

Rewrite the complete factored expression. Polynomial x^{2}-4x+16 is not factored since it does not have any rational roots.

$$\sqrt{2}\left(x^{2}-4x+16\right)$$