Algebra Examples

$(3 x^{2} - x - 7) - (5 x^{2} - 4 x - 2) + (x + 3) (x + 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x^{2} - x - 7 - (5 x^{2}) - (- 4 x) - - 2 + (x + 3) (x + 2)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$3 x^{2} - x - 7 - 5 x^{2} - (- 4 x) - - 2 + (x + 3) (x + 2)$

Step 1.2.2

Multiply $- 4$ by $- 1$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x - - 2 + (x + 3) (x + 2)$

Step 1.2.3

Multiply $- 1$ by $- 2$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + (x + 3) (x + 2)$

Step 1.3

Expand $(x + 3) (x + 2)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x (x + 2) + 3 (x + 2)$

Step 1.3.2

Apply the distributive property.

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x \cdot x + x \cdot 2 + 3 (x + 2)$

Step 1.3.3

Apply the distributive property.

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x \cdot x + x \cdot 2 + 3 x + 3 \cdot 2$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x^{2} + x \cdot 2 + 3 x + 3 \cdot 2$

Step 1.4.1.2

Move $2$ to the left of $x$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x^{2} + 2 \cdot x + 3 x + 3 \cdot 2$

Step 1.4.1.3

Multiply $3$ by $2$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x^{2} + 2 x + 3 x + 6$

Step 1.4.2

Add $2 x$ and $3 x$ .

$3 x^{2} - x - 7 - 5 x^{2} + 4 x + 2 + x^{2} + 5 x + 6$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{2}$ from $3 x^{2}$ .

$- 2 x^{2} - x - 7 + 4 x + 2 + x^{2} + 5 x + 6$

Step 2.2

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

$- x^{2} - x - 7 + 4 x + 2 + 5 x + 6$

Step 2.3

Add $- x$ and $4 x$ .

$- x^{2} + 3 x - 7 + 2 + 5 x + 6$

Step 2.4

Add $3 x$ and $5 x$ .

$- x^{2} + 8 x - 7 + 2 + 6$

Step 2.5

Simplify by adding numbers.

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Step 2.5.1

Add $- 7$ and $2$ .

$- x^{2} + 8 x - 5 + 6$

Step 2.5.2

Add $- 5$ and $6$ .

$- x^{2} + 8 x + 1$