Precalculus Examples

${(a + h)}^{2} + 6$

Step 1

Rewrite ${(a + h)}^{2}$ as $(a + h) (a + h)$ .

$(a + h) (a + h) + 6$

Step 2

Expand $(a + h) (a + h)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$a (a + h) + h (a + h) + 6$

Step 2.2

Apply the distributive property.

$a \cdot a + a h + h (a + h) + 6$

Step 2.3

Apply the distributive property.

$a \cdot a + a h + h a + h \cdot h + 6$

$a \cdot a + a h + h a + h \cdot h + 6$

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 $a$ by $a$ .

$a^{2} + a h + h a + h \cdot h + 6$

Step 3.1.2

Multiply $h$ by $h$ .

$a^{2} + a h + h a + h^{2} + 6$

$a^{2} + a h + h a + h^{2} + 6$

Step 3.2

Add $a h$ and $h a$ .

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Step 3.2.1

Reorder $h$ and $a$ .

$a^{2} + a h + a h + h^{2} + 6$

Step 3.2.2

Add $a h$ and $a h$ .

$a^{2} + 2 a h + h^{2} + 6$

$a^{2} + 2 a h + h^{2} + 6$

$a^{2} + 2 a h + h^{2} + 6$

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