Algebra Examples

${(3 x + 3)}^{2} + (x + 5) (x - 4)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$(3 x + 3) (3 x + 3) + (x + 5) (x - 4)$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$3 x (3 x + 3) + 3 (3 x + 3) + (x + 5) (x - 4)$

Step 1.2.2

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 3 + 3 (3 x + 3) + (x + 5) (x - 4)$

Step 1.2.3

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.2

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

Tap for more steps...

Step 1.3.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.3

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.4

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 3 (3 x) + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.5

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 9 x + 3 \cdot 3 + (x + 5) (x - 4)$

Step 1.3.1.6

Multiply $3$ by $3$ .

$9 x^{2} + 9 x + 9 x + 9 + (x + 5) (x - 4)$

Step 1.3.2

Add $9 x$ and $9 x$ .

$9 x^{2} + 18 x + 9 + (x + 5) (x - 4)$

Step 1.4

Expand $(x + 5) (x - 4)$ using the FOIL Method.

Tap for more steps...

Step 1.4.1

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x (x - 4) + 5 (x - 4)$

Step 1.4.2

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x \cdot x + x \cdot - 4 + 5 (x - 4)$

Step 1.4.3

Apply the distributive property.

$9 x^{2} + 18 x + 9 + x \cdot x + x \cdot - 4 + 5 x + 5 \cdot - 4$

Step 1.5

Simplify and combine like terms.

Tap for more steps...

Step 1.5.1

Simplify each term.

Tap for more steps...

Step 1.5.1.1

Multiply $x$ by $x$ .

$9 x^{2} + 18 x + 9 + x^{2} + x \cdot - 4 + 5 x + 5 \cdot - 4$

Step 1.5.1.2

Move $- 4$ to the left of $x$ .

$9 x^{2} + 18 x + 9 + x^{2} - 4 \cdot x + 5 x + 5 \cdot - 4$

Step 1.5.1.3

Multiply $5$ by $- 4$ .

$9 x^{2} + 18 x + 9 + x^{2} - 4 x + 5 x - 20$

Step 1.5.2

Add $- 4 x$ and $5 x$ .

$9 x^{2} + 18 x + 9 + x^{2} + x - 20$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $9 x^{2}$ and $x^{2}$ .

$10 x^{2} + 18 x + 9 + x - 20$

Step 2.2

Add $18 x$ and $x$ .

$10 x^{2} + 19 x + 9 - 20$

Step 2.3

Subtract $20$ from $9$ .

$10 x^{2} + 19 x - 11$