Algebra Examples

$x (10 x - 7) + 11 (10 x - 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x (10 x) + x \cdot - 7 + 11 (10 x - 7)$

Step 1.2

Rewrite using the commutative property of multiplication.

$10 x \cdot x + x \cdot - 7 + 11 (10 x - 7)$

Step 1.3

Move $- 7$ to the left of $x$ .

$10 x \cdot x - 7 \cdot x + 11 (10 x - 7)$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$10 (x \cdot x) - 7 \cdot x + 11 (10 x - 7)$

Step 1.4.2

Multiply $x$ by $x$ .

$10 x^{2} - 7 \cdot x + 11 (10 x - 7)$

$10 x^{2} - 7 x + 11 (10 x - 7)$

Step 1.5

Apply the distributive property.

$10 x^{2} - 7 x + 11 (10 x) + 11 \cdot - 7$

Step 1.6

Multiply $10$ by $11$ .

$10 x^{2} - 7 x + 110 x + 11 \cdot - 7$

Step 1.7

Multiply $11$ by $- 7$ .

$10 x^{2} - 7 x + 110 x - 77$

Step 2

Add $- 7 x$ and $110 x$ .

$10 x^{2} + 103 x - 77$

Step 3

Factor by grouping.

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Step 3.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 10 \cdot - 77 = - 770$ and whose sum is $b = 103$ .

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Step 3.1.1

Factor $103$ out of $103 x$ .

$10 x^{2} + 103 (x) - 77$

Step 3.1.2

Rewrite $103$ as $- 7$ plus $110$

$10 x^{2} + (- 7 + 110) x - 77$

Step 3.1.3

Apply the distributive property.

$10 x^{2} - 7 x + 110 x - 77$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$(10 x^{2} - 7 x) + 110 x - 77$

Step 3.2.2

Factor out the greatest common factor (GCF) from each group.

$x (10 x - 7) + 11 (10 x - 7)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $10 x - 7$ .

$(10 x - 7) (x + 11)$