Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Expand $(4 x + 4) (a x - 1)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Simplify each term.

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Step 1.2.1

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

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Step 1.2.1.1

Move $x$ .

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

Step 1.2.1.2

Multiply $x$ by $x$ .

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

Step 1.2.2

Multiply $- 1$ by $4$ .

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

Step 1.2.3

Multiply $4$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $4 x^{2} a - 4 x + 4 a x - 4 - x^{2} + 4$ .

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Step 2.1.1

Add $- 4$ and $4$ .

$4 x^{2} a - 4 x + 4 a x - x^{2} + 0$

Step 2.1.2

Add $4 x^{2} a - 4 x + 4 a x - x^{2}$ and $0$ .

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

Step 2.2

Reorder.

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Step 2.2.1

Move $x^{2}$ .

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

Step 2.2.2

Move $- 4 x$ .

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