Precalculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Factor ${(4 x + 5)}^{2} \cdot 2 (5 x + 1)$ out of $3 {(4 x + 5)}^{2} \cdot (4 {(5 x + 1)}^{2}) + {(4 x + 5)}^{3} \cdot 2 (5 x + 1) \cdot 5$ .

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Step 2.1

Factor ${(4 x + 5)}^{2} \cdot 2 (5 x + 1)$ out of $3 {(4 x + 5)}^{2} \cdot (4 {(5 x + 1)}^{2})$ .

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

Step 2.2

Factor ${(4 x + 5)}^{2} \cdot 2 (5 x + 1)$ out of ${(4 x + 5)}^{3} \cdot 2 (5 x + 1) \cdot 5$ .

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

Step 2.3

Factor ${(4 x + 5)}^{2} \cdot 2 (5 x + 1)$ out of ${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (3 \cdot (2 (5 x + 1))) + {(4 x + 5)}^{2} \cdot 2 (5 x + 1) ((4 x + 5) \cdot 5)$ .

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

Step 3

Multiply $2$ by $3$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $5$ by $6$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (30 x + 6 \cdot 1 + (4 x + 5) \cdot 5)$

Step 6

Multiply $6$ by $1$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (30 x + 6 + (4 x + 5) \cdot 5)$

Step 7

Apply the distributive property.

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (30 x + 6 + 4 x \cdot 5 + 5 \cdot 5)$

Step 8

Multiply $5$ by $4$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (30 x + 6 + 20 x + 5 \cdot 5)$

Step 9

Multiply $5$ by $5$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (30 x + 6 + 20 x + 25)$

Step 10

Add $30 x$ and $20 x$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (50 x + 6 + 25)$

Step 11

Add $6$ and $25$ .

${(4 x + 5)}^{2} \cdot 2 (5 x + 1) (50 x + 31)$