Solve 5left(x+nright)^2+6left(x+nright)+1

$$5 { \left(x+n \right) }^{ 2 } +6 \left( x+n \right) +1$$

Evaluate

$$\left(x+n+1\right)\left(5x+5n+1\right)$$

Solution Steps

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

$$5\left(x^{2}+2xn+n^{2}\right)+6\left(x+n\right)+1$$

Use the distributive property to multiply 5 by x^{2}+2xn+n^{2}.

$$5x^{2}+10xn+5n^{2}+6\left(x+n\right)+1$$

Use the distributive property to multiply 6 by x+n.

$$5x^{2}+10xn+5n^{2}+6x+6n+1$$

Expand

$$5x^{2}+10nx+6x+5n^{2}+6n+1$$

Solution Steps

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

$$5\left(x^{2}+2xn+n^{2}\right)+6\left(x+n\right)+1$$

Use the distributive property to multiply 5 by x^{2}+2xn+n^{2}.

$$5x^{2}+10xn+5n^{2}+6\left(x+n\right)+1$$

Use the distributive property to multiply 6 by x+n.

$$5x^{2}+10xn+5n^{2}+6x+6n+1$$