Solve (4+xsqrt{3})^2

$$( 4 + x \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$\left(\sqrt{3}x+4\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4+x\sqrt{3}\right)^{2}.

$$16+8x\sqrt{3}+x^{2}\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16+8x\sqrt{3}+x^{2}\times 3$$

Expand

$$3x^{2}+8\sqrt{3}x+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4+x\sqrt{3}\right)^{2}.

$$16+8x\sqrt{3}+x^{2}\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16+8x\sqrt{3}+x^{2}\times 3$$