Algebra Examples

$(3 x - 5) (4 - 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand $(3 x - 5) (4 - 9 x)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$3 x (4 - 9 x) - 5 (4 - 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.1.2

Apply the distributive property.

$3 x \cdot 4 + 3 x (- 9 x) - 5 (4 - 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.1.3

Apply the distributive property.

$3 x \cdot 4 + 3 x (- 9 x) - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $4$ by $3$ .

$12 x + 3 x (- 9 x) - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$12 x + 3 \cdot - 9 x \cdot x - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.3

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

Tap for more steps...

Step 1.2.1.3.1

Move $x$ .

$12 x + 3 \cdot - 9 (x \cdot x) - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.3.2

Multiply $x$ by $x$ .

$12 x + 3 \cdot - 9 x^{2} - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.4

Multiply $3$ by $- 9$ .

$12 x - 27 x^{2} - 5 \cdot 4 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.5

Multiply $- 5$ by $4$ .

$12 x - 27 x^{2} - 20 - 5 (- 9 x) + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.1.6

Multiply $- 9$ by $- 5$ .

$12 x - 27 x^{2} - 20 + 45 x + (2 x + 1) (6 x^{2} + 5)$

Step 1.2.2

Add $12 x$ and $45 x$ .

$57 x - 27 x^{2} - 20 + (2 x + 1) (6 x^{2} + 5)$

Step 1.3

Expand $(2 x + 1) (6 x^{2} + 5)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$57 x - 27 x^{2} - 20 + 2 x (6 x^{2} + 5) + 1 (6 x^{2} + 5)$

Step 1.3.2

Apply the distributive property.

$57 x - 27 x^{2} - 20 + 2 x (6 x^{2}) + 2 x \cdot 5 + 1 (6 x^{2} + 5)$

Step 1.3.3

Apply the distributive property.

$57 x - 27 x^{2} - 20 + 2 x (6 x^{2}) + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

Rewrite using the commutative property of multiplication.

$57 x - 27 x^{2} - 20 + 2 \cdot 6 x \cdot x^{2} + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.2

Multiply $x$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 1.4.2.1

Move $x^{2}$ .

$57 x - 27 x^{2} - 20 + 2 \cdot 6 (x^{2} x) + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.2.2

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 1.4.2.2.1

Raise $x$ to the power of $1$ .

$57 x - 27 x^{2} - 20 + 2 \cdot 6 (x^{2} x^{1}) + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$57 x - 27 x^{2} - 20 + 2 \cdot 6 x^{2 + 1} + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.2.3

Add $2$ and $1$ .

$57 x - 27 x^{2} - 20 + 2 \cdot 6 x^{3} + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.3

Multiply $2$ by $6$ .

$57 x - 27 x^{2} - 20 + 12 x^{3} + 2 x \cdot 5 + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.4

Multiply $5$ by $2$ .

$57 x - 27 x^{2} - 20 + 12 x^{3} + 10 x + 1 (6 x^{2}) + 1 \cdot 5$

Step 1.4.5

Multiply $6 x^{2}$ by $1$ .

$57 x - 27 x^{2} - 20 + 12 x^{3} + 10 x + 6 x^{2} + 1 \cdot 5$

Step 1.4.6

Multiply $5$ by $1$ .

$57 x - 27 x^{2} - 20 + 12 x^{3} + 10 x + 6 x^{2} + 5$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $57 x$ and $10 x$ .

$- 27 x^{2} - 20 + 12 x^{3} + 67 x + 6 x^{2} + 5$

Step 2.2

Add $- 27 x^{2}$ and $6 x^{2}$ .

$- 21 x^{2} - 20 + 12 x^{3} + 67 x + 5$

Step 2.3

Simplify the expression.

Tap for more steps...

Step 2.3.1

Add $- 20$ and $5$ .

$- 21 x^{2} + 12 x^{3} + 67 x - 15$

Step 2.3.2

Reorder $- 21 x^{2}$ and $12 x^{3}$ .

$12 x^{3} - 21 x^{2} + 67 x - 15$