Algebra Examples

$(3 x - 4) (x + 7) - \frac{1}{4} x^{2}$

Step 1

Simplify each term.

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Step 1.1

Expand $(3 x - 4) (x + 7)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$3 x (x + 7) - 4 (x + 7) - \frac{1}{4} x^{2}$

Step 1.1.2

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 7 - 4 (x + 7) - \frac{1}{4} x^{2}$

Step 1.1.3

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 7 - 4 x - 4 \cdot 7 - \frac{1}{4} x^{2}$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 7 - 4 x - 4 \cdot 7 - \frac{1}{4} x^{2}$

Step 1.2.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot 7 - 4 x - 4 \cdot 7 - \frac{1}{4} x^{2}$

Step 1.2.1.2

Multiply $7$ by $3$ .

$3 x^{2} + 21 x - 4 x - 4 \cdot 7 - \frac{1}{4} x^{2}$

Step 1.2.1.3

Multiply $- 4$ by $7$ .

$3 x^{2} + 21 x - 4 x - 28 - \frac{1}{4} x^{2}$

Step 1.2.2

Subtract $4 x$ from $21 x$ .

$3 x^{2} + 17 x - 28 - \frac{1}{4} x^{2}$

Step 1.3

Combine $x^{2}$ and $\frac{1}{4}$ .

$3 x^{2} + 17 x - 28 - \frac{x^{2}}{4}$

Step 2

To write $3 x^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$17 x - 28 + 3 x^{2} \cdot \frac{4}{4} - \frac{x^{2}}{4}$

Step 3

Simplify terms.

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Step 3.1

Combine $3 x^{2}$ and $\frac{4}{4}$ .

$17 x - 28 + \frac{3 x^{2} \cdot 4}{4} - \frac{x^{2}}{4}$

Step 3.2

Combine the numerators over the common denominator.

$17 x - 28 + \frac{3 x^{2} \cdot 4 - x^{2}}{4}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $x^{2}$ out of $3 x^{2} \cdot 4 - x^{2}$ .

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Step 4.1.1.1

Factor $x^{2}$ out of $3 x^{2} \cdot 4$ .

$17 x - 28 + \frac{x^{2} (3 \cdot 4) - x^{2}}{4}$

Step 4.1.1.2

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

$17 x - 28 + \frac{x^{2} (3 \cdot 4) + x^{2} \cdot - 1}{4}$

Step 4.1.1.3

Factor $x^{2}$ out of $x^{2} (3 \cdot 4) + x^{2} \cdot - 1$ .

$17 x - 28 + \frac{x^{2} (3 \cdot 4 - 1)}{4}$

Step 4.1.2

Multiply $3$ by $4$ .

$17 x - 28 + \frac{x^{2} (12 - 1)}{4}$

Step 4.1.3

Subtract $1$ from $12$ .

$17 x - 28 + \frac{x^{2} \cdot 11}{4}$

Step 4.2

Move $11$ to the left of $x^{2}$ .

$17 x - 28 + \frac{11 x^{2}}{4}$

Step 5

Simplify the expression.

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Step 5.1

Move $- 28$ .

$17 x + \frac{11 x^{2}}{4} - 28$

Step 5.2

Reorder $17 x$ and $\frac{11 x^{2}}{4}$ .

$\frac{11 x^{2}}{4} + 17 x - 28$