Algebra Examples

$(x^{2} + 11 x + 28) \cdot \frac{x + 4}{x + 7}$

Step 1

Multiply $x^{2} + 11 x + 28$ by $\frac{x + 4}{x + 7}$ .

$\frac{(x^{2} + 11 x + 28) (x + 4)}{x + 7}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $x^{2} + 11 x + 28$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $28$ and whose sum is $11$ .

$4, 7$

Step 2.1.2

Write the factored form using these integers.

$\frac{(x + 4) (x + 7) (x + 4)}{x + 7}$

Step 2.2

Combine exponents.

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Step 2.2.1

Raise $x + 4$ to the power of $1$ .

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

Step 2.2.2

Raise $x + 4$ to the power of $1$ .

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

Step 2.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.4

Add $1$ and $1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x + 7$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Divide ${(x + 4)}^{2}$ by $1$ .

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

Step 3.2

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$(x + 4) (x + 4)$

Step 4

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

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Step 4.1

Apply the distributive property.

$x (x + 4) + 4 (x + 4)$

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

$x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x$ by $x$ .

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

Step 5.1.2

Move $4$ to the left of $x$ .

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

Step 5.1.3

Multiply $4$ by $4$ .

$x^{2} + 4 x + 4 x + 16$

Step 5.2

Add $4 x$ and $4 x$ .

$x^{2} + 8 x + 16$