Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

Multiply $4$ by $- 1$ .

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

Step 3.2

Multiply $- 2$ by $- 1$ .

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

Step 3.3

Multiply $- 1$ by $3$ .

$3 x^{2} - 4 x^{2} + 2 x - 3 - 2 x + 5$

Step 4

Subtract $4 x^{2}$ from $3 x^{2}$ .

$- x^{2} + 2 x - 3 - 2 x + 5$

Step 5

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

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Step 5.1

Factor $- 1$ out of $- x^{2}$ .

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

Step 5.2

Factor $- 1$ out of $2 x$ .

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

Step 5.3

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 5.4

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

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

Step 5.5

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

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

Step 6

Factor $- 1$ out of $- 2 x + 5$ .

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Step 6.1

Factor $- 1$ out of $- 2 x$ .

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

Step 6.2

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 6.3

Factor $- 1$ out of $- (2 x) - 1 (- 5)$ .

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

Step 7

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

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

Step 8

Add $- 2 x$ and $2 x$ .

$- (x^{2} + 0 + 3 - 5)$

Step 9

Add $x^{2}$ and $0$ .

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

Step 10

Subtract $5$ from $3$ .

$- (x^{2} - 2)$