Algebra Examples

(4 a + x) (a - x)

$(4 a + x) (a - x)$

Step 1

Expand

(4 a + x) (a - x)

$(4 a + x) (a - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

4 a (a - x) + x (a - x)

$4 a (a - x) + x (a - x)$

Step 1.2

Apply the distributive property.

4 a \cdot a + 4 a (- x) + x (a - x)

$4 a \cdot a + 4 a (- x) + x (a - x)$

Step 1.3

Apply the distributive property.

4 a \cdot a + 4 a (- x) + x a + x (- x)

$4 a \cdot a + 4 a (- x) + x a + x (- x)$

4 a \cdot a + 4 a (- x) + x a + x (- x)

$4 a \cdot a + 4 a (- x) + x a + x (- x)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 2.1.1.1

Move

a

$a$ .

4 (a \cdot a) + 4 a (- x) + x a + x (- x)

$4 (a \cdot a) + 4 a (- x) + x a + x (- x)$

Step 2.1.1.2

Multiply

a

$a$ by

a

$a$ .

4 a^{2} + 4 a (- x) + x a + x (- x)

$4 a^{2} + 4 a (- x) + x a + x (- x)$

4 a^{2} + 4 a (- x) + x a + x (- x)

$4 a^{2} + 4 a (- x) + x a + x (- x)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

4 a^{2} + 4 \cdot - 1 a x + x a + x (- x)

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

Step 2.1.3

Multiply

4

$4$ by

- 1

$- 1$ .

4 a^{2} - 4 a x + x a + x (- x)

$4 a^{2} - 4 a x + x a + x (- x)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

4 a^{2} - 4 a x + x a - x \cdot x

$4 a^{2} - 4 a x + x a - x \cdot x$

Step 2.1.5

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.5.1

Move

x

$x$ .

4 a^{2} - 4 a x + x a - (x \cdot x)

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

Step 2.1.5.2

Multiply

x

$x$ by

x

$x$ .

4 a^{2} - 4 a x + x a - x^{2}

$4 a^{2} - 4 a x + x a - x^{2}$

4 a^{2} - 4 a x + x a - x^{2}

$4 a^{2} - 4 a x + x a - x^{2}$

4 a^{2} - 4 a x + x a - x^{2}

$4 a^{2} - 4 a x + x a - x^{2}$

Step 2.2

Add

- 4 a x

$- 4 a x$ and

x a

$x a$ .

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Step 2.2.1

Reorder

x

$x$ and

a

$a$ .

4 a^{2} - 4 a x + a x - x^{2}

$4 a^{2} - 4 a x + a x - x^{2}$

Step 2.2.2

Add

- 4 a x

$- 4 a x$ and

a x

$a x$ .

4 a^{2} - 3 a x - x^{2}

$4 a^{2} - 3 a x - x^{2}$

4 a^{2} - 3 a x - x^{2}

$4 a^{2} - 3 a x - x^{2}$

4 a^{2} - 3 a x - x^{2}

$4 a^{2} - 3 a x - x^{2}$

(4 a + x) (a - x)

$(4 a + x) (a - x)$

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

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