Precalculus Examples

$- {(2 x - 7)}^{2} - 3$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(2 x - 7)}^{2}$ as $(2 x - 7) (2 x - 7)$ .

$- ((2 x - 7) (2 x - 7)) - 3$

Step 1.2

Expand $(2 x - 7) (2 x - 7)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- (2 x (2 x - 7) - 7 (2 x - 7)) - 3$

Step 1.2.2

Apply the distributive property.

$- (2 x (2 x) + 2 x \cdot - 7 - 7 (2 x - 7)) - 3$

Step 1.2.3

Apply the distributive property.

$- (2 x (2 x) + 2 x \cdot - 7 - 7 (2 x) - 7 \cdot - 7) - 3$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$- (2 \cdot 2 x \cdot x + 2 x \cdot - 7 - 7 (2 x) - 7 \cdot - 7) - 3$

Step 1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.2.1

Move $x$ .

$- (2 \cdot 2 (x \cdot x) + 2 x \cdot - 7 - 7 (2 x) - 7 \cdot - 7) - 3$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

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

Step 1.3.1.4

Multiply $- 7$ by $2$ .

$- (4 x^{2} - 14 x - 7 (2 x) - 7 \cdot - 7) - 3$

Step 1.3.1.5

Multiply $2$ by $- 7$ .

$- (4 x^{2} - 14 x - 14 x - 7 \cdot - 7) - 3$

Step 1.3.1.6

Multiply $- 7$ by $- 7$ .

$- (4 x^{2} - 14 x - 14 x + 49) - 3$

Step 1.3.2

Subtract $14 x$ from $- 14 x$ .

$- (4 x^{2} - 28 x + 49) - 3$

Step 1.4

Apply the distributive property.

$- (4 x^{2}) - (- 28 x) - 1 \cdot 49 - 3$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $4$ by $- 1$ .

$- 4 x^{2} - (- 28 x) - 1 \cdot 49 - 3$

Step 1.5.2

Multiply $- 28$ by $- 1$ .

$- 4 x^{2} + 28 x - 1 \cdot 49 - 3$

Step 1.5.3

Multiply $- 1$ by $49$ .

$- 4 x^{2} + 28 x - 49 - 3$

Step 2

Subtract $3$ from $- 49$ .

$- 4 x^{2} + 28 x - 52$