Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

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

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Step 2.2.1.1.1

Move $x$ .

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

Step 2.2.1.1.2

Multiply $x$ by $x$ .

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

Step 2.2.1.2

Multiply $7$ by $3$ .

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

Step 2.2.1.3

Multiply $- 4$ by $7$ .

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

Step 2.2.2

Subtract $4 x$ from $21 x$ .

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

Step 2.3

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

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

Step 3

Reorder.

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Step 3.1

Move $- 28$ .

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

Step 3.2

Move $17 x$ .

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

Step 4

Reorder terms.

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

Step 5

Remove parentheses.

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