Algebra Examples

$5 (x + 3) (x + 2) - 3 (x^{2} + 2 x + 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$(5 x + 5 \cdot 3) (x + 2) - 3 (x^{2} + 2 x + 1)$

Step 1.2

Multiply $5$ by $3$ .

$(5 x + 15) (x + 2) - 3 (x^{2} + 2 x + 1)$

Step 1.3

Expand $(5 x + 15) (x + 2)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$5 x (x + 2) + 15 (x + 2) - 3 (x^{2} + 2 x + 1)$

Step 1.3.2

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 2 + 15 (x + 2) - 3 (x^{2} + 2 x + 1)$

Step 1.3.3

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 2 + 15 x + 15 \cdot 2 - 3 (x^{2} + 2 x + 1)$

Step 1.4

Simplify and combine like terms.

Tap for more steps...

Step 1.4.1

Simplify each term.

Tap for more steps...

Step 1.4.1.1

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

Tap for more steps...

Step 1.4.1.1.1

Move $x$ .

$5 (x \cdot x) + 5 x \cdot 2 + 15 x + 15 \cdot 2 - 3 (x^{2} + 2 x + 1)$

Step 1.4.1.1.2

Multiply $x$ by $x$ .

$5 x^{2} + 5 x \cdot 2 + 15 x + 15 \cdot 2 - 3 (x^{2} + 2 x + 1)$

Step 1.4.1.2

Multiply $2$ by $5$ .

$5 x^{2} + 10 x + 15 x + 15 \cdot 2 - 3 (x^{2} + 2 x + 1)$

Step 1.4.1.3

Multiply $15$ by $2$ .

$5 x^{2} + 10 x + 15 x + 30 - 3 (x^{2} + 2 x + 1)$

Step 1.4.2

Add $10 x$ and $15 x$ .

$5 x^{2} + 25 x + 30 - 3 (x^{2} + 2 x + 1)$

Step 1.5

Apply the distributive property.

$5 x^{2} + 25 x + 30 - 3 x^{2} - 3 (2 x) - 3 \cdot 1$

Step 1.6

Simplify.

Tap for more steps...

Step 1.6.1

Multiply $2$ by $- 3$ .

$5 x^{2} + 25 x + 30 - 3 x^{2} - 6 x - 3 \cdot 1$

Step 1.6.2

Multiply $- 3$ by $1$ .

$5 x^{2} + 25 x + 30 - 3 x^{2} - 6 x - 3$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $3 x^{2}$ from $5 x^{2}$ .

$2 x^{2} + 25 x + 30 - 6 x - 3$

Step 2.2

Subtract $6 x$ from $25 x$ .

$2 x^{2} + 19 x + 30 - 3$

Step 2.3

Subtract $3$ from $30$ .

$2 x^{2} + 19 x + 27$