Precalculus Examples

$7 {(3 x + 2)}^{2} {(1 - x)}^{2} + (3 x + 2) {(1 - x)}^{3}$

Step 1

Factor $(3 x + 2) {(1 - x)}^{2}$ out of $7 {(3 x + 2)}^{2} {(1 - x)}^{2} + (3 x + 2) {(1 - x)}^{3}$ .

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Step 1.1

Factor $(3 x + 2) {(1 - x)}^{2}$ out of $7 {(3 x + 2)}^{2} {(1 - x)}^{2}$ .

$(3 x + 2) {(1 - x)}^{2} (7 (3 x + 2)) + (3 x + 2) {(1 - x)}^{3}$

Step 1.2

Factor $(3 x + 2) {(1 - x)}^{2}$ out of $(3 x + 2) {(1 - x)}^{3}$ .

$(3 x + 2) {(1 - x)}^{2} (7 (3 x + 2)) + (3 x + 2) {(1 - x)}^{2} (1 - x)$

Step 1.3

Factor $(3 x + 2) {(1 - x)}^{2}$ out of $(3 x + 2) {(1 - x)}^{2} (7 (3 x + 2)) + (3 x + 2) {(1 - x)}^{2} (1 - x)$ .

$(3 x + 2) {(1 - x)}^{2} (7 (3 x + 2) + 1 - x)$

Step 2

Apply the distributive property.

$(3 x + 2) {(1 - x)}^{2} (7 (3 x) + 7 \cdot 2 + 1 - x)$

Step 3

Multiply $3$ by $7$ .

$(3 x + 2) {(1 - x)}^{2} (21 x + 7 \cdot 2 + 1 - x)$

Step 4

Multiply $7$ by $2$ .

$(3 x + 2) {(1 - x)}^{2} (21 x + 14 + 1 - x)$

Step 5

Subtract $x$ from $21 x$ .

$(3 x + 2) {(1 - x)}^{2} (20 x + 14 + 1)$

Step 6

Add $14$ and $1$ .

$(3 x + 2) {(1 - x)}^{2} (20 x + 15)$

Step 7

Factor.

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Step 7.1

Factor $5$ out of $20 x + 15$ .

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Step 7.1.1

Factor $5$ out of $20 x$ .

$(3 x + 2) {(1 - x)}^{2} (5 (4 x) + 15)$

Step 7.1.2

Factor $5$ out of $15$ .

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

Step 7.1.3

Factor $5$ out of $5 (4 x) + 5 (3)$ .

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

Step 7.2

Remove unnecessary parentheses.

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