Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 3$ by $4$ .

$4 x^{2} - 12 x + 4 \cdot 5 - 3 (x^{2} - 2 x + 1)$

Step 1.2.2

Multiply $4$ by $5$ .

$4 x^{2} - 12 x + 20 - 3 (x^{2} - 2 x + 1)$

Step 1.3

Apply the distributive property.

$4 x^{2} - 12 x + 20 - 3 x^{2} - 3 (- 2 x) - 3 \cdot 1$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $- 2$ by $- 3$ .

$4 x^{2} - 12 x + 20 - 3 x^{2} + 6 x - 3 \cdot 1$

Step 1.4.2

Multiply $- 3$ by $1$ .

$4 x^{2} - 12 x + 20 - 3 x^{2} + 6 x - 3$

Step 2

Simplify by adding terms.

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Step 2.1

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

$x^{2} - 12 x + 20 + 6 x - 3$

Step 2.2

Add $- 12 x$ and $6 x$ .

$x^{2} - 6 x + 20 - 3$

Step 2.3

Subtract $3$ from $20$ .

$x^{2} - 6 x + 17$