Precalculus Examples

$(4 s) (2 s) - 4 s \cdot 5 + (1) (2 s) - 1 \cdot 5$

Step 1

Regroup terms.

$- 4 s \cdot 5 + (4 s) (2 s) + (1) (2 s) - 1 \cdot 5$

Step 2

Multiply $5$ by $- 4$ .

$- 20 s + (4 s) (2 s) + (1) (2 s) - 1 \cdot 5$

Step 3

Rewrite using the commutative property of multiplication.

$- 20 s + 4 \cdot 2 s \cdot s + (1) (2 s) - 1 \cdot 5$

Step 4

Multiply $s$ by $s$ by adding the exponents.

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Step 4.1

Move $s$ .

$- 20 s + 4 \cdot 2 (s \cdot s) + (1) (2 s) - 1 \cdot 5$

Step 4.2

Multiply $s$ by $s$ .

$- 20 s + 4 \cdot 2 s^{2} + (1) (2 s) - 1 \cdot 5$

Step 5

Multiply $4$ by $2$ .

$- 20 s + 8 s^{2} + (1) (2 s) - 1 \cdot 5$

Step 6

Multiply $2 s$ by $1$ .

$- 20 s + 8 s^{2} + 2 s - 1 \cdot 5$

Step 7

Multiply $- 1$ by $5$ .

$- 20 s + 8 s^{2} + 2 s - 5$

Step 8

Reorder terms.

$8 s^{2} + 2 s - 20 s - 5$

Step 9

Factor out the greatest common factor from each group.

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Step 9.1

Group the first two terms and the last two terms.

$(8 s^{2} + 2 s) - 20 s - 5$

Step 9.2

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

$2 s (4 s + 1) - 5 (4 s + 1)$

Step 10

Factor the polynomial by factoring out the greatest common factor, $4 s + 1$ .

$(4 s + 1) (2 s - 5)$