Algebra Examples

$6 x^{2} + 10 x - 1$ and $- 5 x^{2} - 2 x + 1$

Step 1

Subtract the second expression $- 5 x^{2} - 2 x + 1$ from the first expression $6 x^{2} + 10 x - 1$ .

$6 x^{2} + 10 x - 1 - (- 5 x^{2} - 2 x + 1)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$6 x^{2} + 10 x - 1 - (- 5 x^{2}) - (- 2 x) - 1 \cdot 1$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 5$ by $- 1$ .

$6 x^{2} + 10 x - 1 + 5 x^{2} - (- 2 x) - 1 \cdot 1$

Step 2.2.2

Multiply $- 2$ by $- 1$ .

$6 x^{2} + 10 x - 1 + 5 x^{2} + 2 x - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$6 x^{2} + 10 x - 1 + 5 x^{2} + 2 x - 1$

Step 3

Simplify by adding terms.

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Step 3.1

Add $6 x^{2}$ and $5 x^{2}$ .

$11 x^{2} + 10 x - 1 + 2 x - 1$

Step 3.2

Add $10 x$ and $2 x$ .

$11 x^{2} + 12 x - 1 - 1$

Step 3.3

Subtract $1$ from $- 1$ .

$11 x^{2} + 12 x - 2$