Simplify (x+h)^2+1

${(x + h)}^{2} + 1$

Simplify each term.

Rewrite ${(x + h)}^{2}$ as $(x + h) (x + h)$ .

$(x + h) (x + h) + 1$

Expand $(x + h) (x + h)$ using the FOIL Method.

Apply the distributive property.

$x (x + h) + h (x + h) + 1$

Apply the distributive property.

$x \cdot x + x h + h (x + h) + 1$

Apply the distributive property.

$x \cdot x + x h + h x + h \cdot h + 1$

$x \cdot x + x h + h x + h \cdot h + 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x h + h x + h \cdot h + 1$

Multiply $h$ by $h$ .

$x^{2} + x h + h x + h^{2} + 1$

$x^{2} + x h + h x + h^{2} + 1$

Add $x h$ and $h x$ .

Reorder $x$ and $h$ .

$x^{2} + h x + h x + h^{2} + 1$

Add $h x$ and $h x$ .

$x^{2} + 2 h x + h^{2} + 1$

$x^{2} + 2 h x + h^{2} + 1$

$x^{2} + 2 h x + h^{2} + 1$

$x^{2} + 2 h x + h^{2} + 1$

Simplify the expression.

Move $x^{2}$ .

$2 h x + h^{2} + x^{2} + 1$

Reorder $2 h x$ and $h^{2}$ .

$h^{2} + 2 h x + x^{2} + 1$

$h^{2} + 2 h x + x^{2} + 1$

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