Evaluate 3(x+h)^2+4(x+h)-2

$3 {(x + h)}^{2} + 4 (x + h) - 2$

Step 1

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

$3 ((x + h) (x + h)) + 4 (x + h) - 2$

Step 2

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

Apply the distributive property.

$3 (x (x + h) + h (x + h)) + 4 (x + h) - 2$

Apply the distributive property.

$3 (x \cdot x + x h + h (x + h)) + 4 (x + h) - 2$

Apply the distributive property.

$3 (x \cdot x + x h + h x + h \cdot h) + 4 (x + h) - 2$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x h + h x + h \cdot h) + 4 (x + h) - 2$

Multiply $h$ by $h$ .

$3 (x^{2} + x h + h x + h^{2}) + 4 (x + h) - 2$

Add $x h$ and $h x$ .

Reorder $x$ and $h$ .

$3 (x^{2} + h x + h x + h^{2}) + 4 (x + h) - 2$

Add $h x$ and $h x$ .

$3 (x^{2} + 2 h x + h^{2}) + 4 (x + h) - 2$

Step 4

Apply the distributive property.

$3 x^{2} + 3 (2 h x) + 3 h^{2} + 4 (x + h) - 2$

Step 5

Multiply $2$ by $3$ .

$3 x^{2} + 6 (h x) + 3 h^{2} + 4 (x + h) - 2$

Step 6

Apply the distributive property.

$3 x^{2} + 6 h x + 3 h^{2} + 4 x + 4 h - 2$