Algebra Examples

$\frac{10 x^{2} - 40 x}{x^{2} + 3 x - 28} \cdot \frac{x^{2} + 6 x - 7}{13 x^{2}}$

Step 1

Factor $10 x$ out of $10 x^{2} - 40 x$ .

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Step 1.1

Factor $10 x$ out of $10 x^{2}$ .

$\frac{10 x (x) - 40 x}{x^{2} + 3 x - 28} \cdot \frac{x^{2} + 6 x - 7}{13 x^{2}}$

Step 1.2

Factor $10 x$ out of $- 40 x$ .

$\frac{10 x (x) + 10 x (- 4)}{x^{2} + 3 x - 28} \cdot \frac{x^{2} + 6 x - 7}{13 x^{2}}$

Step 1.3

Factor $10 x$ out of $10 x (x) + 10 x (- 4)$ .

$\frac{10 x (x - 4)}{x^{2} + 3 x - 28} \cdot \frac{x^{2} + 6 x - 7}{13 x^{2}}$

Step 2

Factor $x^{2} + 3 x - 28$ using the AC method.

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Step 2.1

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 $3$ .

$- 4, 7$

Step 2.2

Write the factored form using these integers.

$\frac{10 x (x - 4)}{(x - 4) (x + 7)} \cdot \frac{x^{2} + 6 x - 7}{13 x^{2}}$

Step 3

Factor $x^{2} + 6 x - 7$ using the AC method.

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Step 3.1

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 $- 7$ and whose sum is $6$ .

$- 1, 7$

Step 3.2

Write the factored form using these integers.

$\frac{10 x (x - 4)}{(x - 4) (x + 7)} \cdot \frac{(x - 1) (x + 7)}{13 x^{2}}$

Step 4

Simplify terms.

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Step 4.1

Combine.

$\frac{10 x (x - 4) ((x - 1) (x + 7))}{(x - 4) (x + 7) (13 x^{2})}$

Step 4.2

Cancel the common factor of $x$ and $x^{2}$ .

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Step 4.2.1

Factor $x$ out of $10 x (x - 4) ((x - 1) (x + 7))$ .

$\frac{x ((10 (x - 4)) ((x - 1) (x + 7)))}{(x - 4) (x + 7) (13 x^{2})}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $x$ out of $(x - 4) (x + 7) (13 x^{2})$ .

$\frac{x ((10 (x - 4)) ((x - 1) (x + 7)))}{x ((x - 4) (x + 7) (13 x))}$

Step 4.2.2.2

Cancel the common factor.

$\frac{x ((10 (x - 4)) ((x - 1) (x + 7)))}{x ((x - 4) (x + 7) (13 x))}$

Step 4.2.2.3

Rewrite the expression.

$\frac{(10 (x - 4)) ((x - 1) (x + 7))}{(x - 4) (x + 7) (13 x)}$

Step 4.3

Cancel the common factor of $x - 4$ .

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Step 4.3.1

Cancel the common factor.

$\frac{10 (x - 4) ((x - 1) (x + 7))}{(x - 4) (x + 7) (13 x)}$

Step 4.3.2

Rewrite the expression.

$\frac{(10) ((x - 1) (x + 7))}{(x + 7) (13 x)}$

Step 4.4

Cancel the common factor of $x + 7$ .

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Step 4.4.1

Cancel the common factor.

$\frac{10 ((x - 1) (x + 7))}{(x + 7) (13 x)}$

Step 4.4.2

Rewrite the expression.

$\frac{(10) (x - 1)}{13 x}$

$\frac{10 (x - 1)}{13 x}$