Algebra Examples

$x (4 x - 5) + 9 (4 x - 5)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$x (4 x) + x \cdot - 5 + 9 (4 x - 5)$

Step 1.2

Rewrite using the commutative property of multiplication.

$4 x \cdot x + x \cdot - 5 + 9 (4 x - 5)$

Step 1.3

Move $- 5$ to the left of $x$ .

$4 x \cdot x - 5 \cdot x + 9 (4 x - 5)$

Step 1.4

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

Tap for more steps...

Step 1.4.1

Move $x$ .

$4 (x \cdot x) - 5 \cdot x + 9 (4 x - 5)$

Step 1.4.2

Multiply $x$ by $x$ .

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

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Multiply $4$ by $9$ .

$4 x^{2} - 5 x + 36 x + 9 \cdot - 5$

Step 1.7

Multiply $9$ by $- 5$ .

$4 x^{2} - 5 x + 36 x - 45$

Step 2

Add $- 5 x$ and $36 x$ .

$4 x^{2} + 31 x - 45$

Step 3

Factor by grouping.

Tap for more steps...

Step 3.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 45 = - 180$ and whose sum is $b = 31$ .

Tap for more steps...

Step 3.1.1

Factor $31$ out of $31 x$ .

$4 x^{2} + 31 (x) - 45$

Step 3.1.2

Rewrite $31$ as $- 5$ plus $36$

$4 x^{2} + (- 5 + 36) x - 45$

Step 3.1.3

Apply the distributive property.

$4 x^{2} - 5 x + 36 x - 45$

Step 3.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 3.2.1

Group the first two terms and the last two terms.

$(4 x^{2} - 5 x) + 36 x - 45$

Step 3.2.2

Factor out the greatest common factor (GCF) from each group.

$x (4 x - 5) + 9 (4 x - 5)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $4 x - 5$ .

$(4 x - 5) (x + 9)$