Pre-Algebra Examples

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

Step 1

Write $(x - 3) (x - 7)$ as an equation.

$y = (x - 3) (x - 7)$

Step 2

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

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Step 2.1

Apply the distributive property.

$y = x (x - 7) - 3 (x - 7)$

Step 2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 7 - 3 (x - 7)$

Step 2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 7 - 3 x - 3 \cdot - 7$

$y = x \cdot x + x \cdot - 7 - 3 x - 3 \cdot - 7$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 7 - 3 x - 3 \cdot - 7$

Step 3.1.2

Move $- 7$ to the left of $x$ .

$y = x^{2} - 7 \cdot x - 3 x - 3 \cdot - 7$

Step 3.1.3

Multiply $- 3$ by $- 7$ .

$y = x^{2} - 7 x - 3 x + 21$

$y = x^{2} - 7 x - 3 x + 21$

Step 3.2

Subtract $3 x$ from $- 7 x$ .

$y = x^{2} - 10 x + 21$

$y = x^{2} - 10 x + 21$

Step 4

When solving for $y$ , $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$