Precalculus Examples

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

Step 1

Rewrite ${(3 x + h)}^{2}$ as $(3 x + h) (3 x + h)$ .

$(3 x + h) (3 x + h) + 3 x$

Step 2

Expand $(3 x + h) (3 x + h)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 x (3 x + h) + h (3 x + h) + 3 x$

Step 2.2

Apply the distributive property.

$3 x (3 x) + 3 x h + h (3 x + h) + 3 x$

Step 2.3

Apply the distributive property.

$3 x (3 x) + 3 x h + h (3 x) + h \cdot h + 3 x$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x h + h (3 x) + h \cdot h + 3 x$

Step 3.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x h + h (3 x) + h \cdot h + 3 x$

Step 3.1.2.2

Multiply $x$ by $x$ .

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

Step 3.1.3

Multiply $3$ by $3$ .

$9 x^{2} + 3 x h + h (3 x) + h \cdot h + 3 x$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 x h + 3 h x + h \cdot h + 3 x$

Step 3.1.5

Multiply $h$ by $h$ .

$9 x^{2} + 3 x h + 3 h x + h^{2} + 3 x$

Step 3.2

Add $3 x h$ and $3 h x$ .

Tap for more steps...

Step 3.2.1

Move $x$ .

$9 x^{2} + 3 h x + 3 h x + h^{2} + 3 x$

Step 3.2.2

Add $3 h x$ and $3 h x$ .

$9 x^{2} + 6 h x + h^{2} + 3 x$