Finite Math Examples

$y = - 8 {(3 x + 2)}^{3} {(4 x + 3)}^{- 3} + 9 {(3 x + 2)}^{2} {(4 x + 3)}^{- 2}$

Step 1

Factor ${(3 x + 2)}^{2} {(4 x + 3)}^{- 3}$ out of $- 8 {(3 x + 2)}^{3} {(4 x + 3)}^{- 3} + 9 {(3 x + 2)}^{2} {(4 x + 3)}^{- 2}$ .

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Step 1.1

Factor ${(3 x + 2)}^{2} {(4 x + 3)}^{- 3}$ out of $- 8 {(3 x + 2)}^{3} {(4 x + 3)}^{- 3}$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 8 (3 x + 2)) + 9 {(3 x + 2)}^{2} {(4 x + 3)}^{- 2}$

Step 1.2

Factor ${(3 x + 2)}^{2} {(4 x + 3)}^{- 3}$ out of $9 {(3 x + 2)}^{2} {(4 x + 3)}^{- 2}$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 8 (3 x + 2)) + {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (9 (4 x + 3))$

Step 1.3

Factor ${(3 x + 2)}^{2} {(4 x + 3)}^{- 3}$ out of ${(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 8 (3 x + 2)) + {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (9 (4 x + 3))$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 8 (3 x + 2) + 9 (4 x + 3))$

Step 2

Apply the distributive property.

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 8 (3 x) - 8 \cdot 2 + 9 (4 x + 3))$

Step 3

Multiply $3$ by $- 8$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 24 x - 8 \cdot 2 + 9 (4 x + 3))$

Step 4

Multiply $- 8$ by $2$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 24 x - 16 + 9 (4 x + 3))$

Step 5

Apply the distributive property.

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 24 x - 16 + 9 (4 x) + 9 \cdot 3)$

Step 6

Multiply $4$ by $9$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 24 x - 16 + 36 x + 9 \cdot 3)$

Step 7

Multiply $9$ by $3$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (- 24 x - 16 + 36 x + 27)$

Step 8

Add $- 24 x$ and $36 x$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (12 x - 16 + 27)$

Step 9

Add $- 16$ and $27$ .

$y = {(3 x + 2)}^{2} {(4 x + 3)}^{- 3} (12 x + 11)$